Thermodynamics of protein-ligand interactions seems to be associated to a narrow range of Gibbs Free Energy. As a consequence, a linear enthalpy-entropy relationship showing an apparent Enthalpy-Entropy compensation (EEC) is frequently observed associated to the study of protein-ligand interactions. This EEC affects negatively the design and discovery of new and more efficient drugs capable of binding protein-targets with a higher affinity. Originally attributed to experimental errors, compensation between H and TS values is a real observable fact, although its molecular origin has remained obscure and controversial. Herein we show the results of a data search of G values of 2558 protein-ligand interactions and 3025 “in vivo” ligand concentrations from the Protein Data Bank bind Database and the Metabolome Data Base (2020). These results, together with the mechano-statistical interpretation of the thermodynamic properties leads to the conclusion that the EEC has no basis in statistical thermodynamics. It can be plausibly explained as a consequence of the narrow range of G associated to protein-ligand interactions. The Gaussian distribution of the G values matches very well with that of ligands. These results suggest the hypothesis that the set of G values for the protein-ligand interactions is the result of the evolution of proteins. The conformation versatility of present proteins and the exchange of thousands (even millions) of minute amounts of energy with the environment may have functioned as a homeostatic mechanism to make G of proteins adaptive to changes in availability of ligands, and therefore achieve the maximum regulatory capacity of the protein function. Finally, a plausible strategy to avoid the EEC is suggested.

We used the complete set of convex pentagons enabling filing the plane without any overlaps or gaps (including the Marjorie Rice tiles) as generators of Voronoi tessellations. Shannon entropy of the tessellations was calculated. Some of the basic mosaics are flexible and give rise to a diversity of Voronoi tessellations. The Shannon entropy of these tessellations varied in a broad range. Voronoi tessellation, emerging from the basic pentagonal tiling built from hexagons only, was revealed (the Shannon entropy of this tiling is zero). Decagons and hendecagon did not appear in the studied Voronoi diagrams. The most abundant Voronoi tessellations are built from three different kinds of polygons. The most widespread is the combination of pentagons, hexagons and heptagons. The most abundant polygons are pentagons and hexagons. No Voronoi tiling built only of pentagons was registered. Flexible basic pentagonal mosaics give rise to a diversity of Voronoi tessellations, which are characterized by the same symmetry group; however, the coordination number of the vertices is variable. These Voronoi tessellations may be useful for the interpretation of the iso-symmetrical phase transitions.

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences, and distinguishability, and is formalized using the distinctions (`dits') of a partition (a pair of points distinguished by the partition). All the definitions of simple, joint, conditional, and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates (cohered together in the pure superposition state being measured) that are distinguished by the measurement (decohered in the post-measurement mixed state). Both the classical and quantum versions of logical entropy have simple interpretations as "two-draw" probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states.

A numerical method using combined detached-eddy simulation (DES) and cavitation model considering the rotation effect is used for unsteady cavitation flow field of the centrifugal pump. Closed type pump test system was established to obtain the pump performance and pressure pulsation characteristics under different flow rates and cavitation condition, which provide boundary conditions and verification of calculations. Based on the calculation results of the unsteady flow field of the centrifugal pump cavitation, the entropy generation analysis of the flow field and the pressure fluctuation characteristics were carried out. Then the relationship between cavitation and the deterioration of the centrifugal pump performance and the generation of the unstable operation excitation force was tried to reveal. The internal energy loss is mainly concentrated in the impeller, volute, and pump cavity area, which accounts for more than 85% of the total entropy generation. The characteristic frequency of about 0.333 Strouhal Number appears at the volute tongue due to the cavitation flow spread downstream.

The entropy models have been recently adopted in many studies to evaluate the distribution of the shear stress in circular channels. However, the uncertainty in their predictions and their reliability remains an open question. We present a novel method to evaluate the uncertainty of four popular entropy models, including Shannon, Shannon-Power Low (PL), Tsallis, and Renyi, in shear stress estimation in circular channels. The Bayesian Monte-Carlo (BMC) uncertainty method is simplified considering a 95% Confidence Bound (CB). We developed a new statistic index called as FREE_opt-based OCB (FOCB) using the statistical indices Forecasting Range of Error Estimation (FREE) and the percentage of observed data in the CB (N_in), which integrates their combined effect. The Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, had the highest certainty in the calculation of shear stress values in circular channels followed by traditional uniform flow shear stress and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy with much higher values of FOCB equal to 57.726 has less certainty in the estimation of shear stress than other models. Using the presented results in this study, the amount of confidence in entropy methods in the calculation of shear stress to design and implement different types of open channels and their stability is determined.

Ultraviolet light incident on organic material can initiate its spontaneous dissipative structuring into chromophores which can catalyze their own replication. This may have been the case for one of the most ancient of all chromophores dissipating the Archean UVC photon flux, the nucleic acids. Oligos of nucleic acids with affinity to particular amino acids which foment UVC photon dissipation would have been selected through non-equilibrium thermodynamic imperatives which favor entropy production. Indeed, we show here that those amino acids with characteristics most relevant to fomenting UVC photon dissipation are precisely those with greatest chemical affinity to their codons or anticodons. Entropy production could thus provide an explanation for the accumulation of information in nucleic acids relevant to the dissipation of the externally imposed thermodynamic potentials. The accumulation of information in this manner provides a link between evolution and entropy production.

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. In our model, the condensed polyelectrolytes are taken to be doubly charged dimers of length comparable to the distance between sites along the phosphate chains. Within this lattice-gas model, each adsorption site is assumed to have either a vacancy or a positively-charged dimer attached with the dimer oriented either parallel or perpendicular to the double helix DNA chain. We find that the inclusion of the fluctuation terms decreases the entropy by ∼50% in the weak binding regime. There, the bound dimer concentration is low because the dimers are repelled from the DNA molecule, which competes with the chemical potential driving them from the solution to the DNA surface. Surprisingly, this decrease in entropy due to correlations is so significant that it overcompensates for the entropy increase at the mean field level, so that the total entropy is even lower than in the absence of interactions between lattice sites. As a bonus, we present a transparent exposition of the methods used that could be useful to students and others wishing to use this formulation to extend this calculation to more realistic models.

Is it possible to quantify in General Relativity, GR, the entropy generated by supermassive black holes, BHs, during its evaporation time, since the intrinsic Hawking radiation in the infinity that, although insignificant, is important in the effects on the thermal quantum atmosphere?The purpose was to develop a formula that allows us to measure the entropy generated during the evaporation time of different types of BHs of: i. remnant BH of the binary black holes’ merger, BBH: GW150914, GW151226 and LTV151012 detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO), and ii. Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman, and thus quantify in GR the “insignificant” quantum effects involved, in order to contribute to the validity of the generalized second law (GSL) that directly links the laws of black hole mechanics to the ordinary laws of thermodynamics, as a starting point for unifying quantum effects with GR. This formula could have some relationship with the detection of the shadow’s image of the event horizon of a BH.This formula was developed in dimensional analysis, using the constants of nature and the possible evaporation time of a black hole, to quantify the entropy generated during that time. The energy-stress tensor was calculated with the 4 metrics to obtain the material content and apply the proposed formula.The entropy of the evaporation time of BHs proved to be insignificant, its temperature is barely above absolute zero, however, the calculation of this type of entropy allows us to argue about the importance of the quantum effects of Hawking radiation mentioned by authors who have studied the quantum effects with arguments that are fundamentally based on the presence of the surrounding thermal atmosphere of the black hole.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

Bayesian Maximum Entropy (BME) is increasingly used in predicting and mapping spatio-temporal data. However, studies that have fully evaluated its robustness empirically are rare. Therefore, this research examined empirically the effect of skewness, sample size and spatial dependency level using simulated data. We considered symmetric data, data positively skewed by 1, 3, 6 and 9, data with weak, moderate, and strong spatial dependency levels, and sample sizes from 100 to 500 at the interval length of 50. The results showed that the variation of sample sizes and spatial dependency levels do not affect the Mean Square Error (MSE) and bias of BME prediction. However, skewness affects the MSE of prediction but does not affect the bias. This result indicates that BME is robust to sample size and is unbiased. Despite the significant difference due to skewness, a graphical plot showed values of MSE close to zero, suggesting that BME can be considered robust to skewness.

We consider the conjecture of the relationship between the entanglement entropy of spacetime, matter and the action in Einstein's general relativity. Our analysis suggests the possibility of regarding the entanglement entropy of spacetime and matter as the dimensionless action in general relativity by using Planck units. In this case, the action principle originates from the maximization of the entanglement entropy. We also show that the fundamental property of entanglement entropy leads to attractive characteristic of gravitational force for classical particles.

An overview of the link between nonequilibrium thermodynamics and complexity theory is offered. It is shown how the rate of entropy production can be quantified through the spectrum of the Lyapunov exponents. It was shown how the entropy production per unit of time meets the necessary and sufficient conditions to be a Lyapunov function and constitutes per se an extremal principle. The entropy production fractal dimension conjecture was established. It is shown how the rate of entropy production as a non-extremal criterion represents an alternative way of sensitivity analysis of differential equations. Finally, an extension to biophysical-chemical systems, on the one hand, the use of the dissipation function is shown, as a thermodynamic potential out of equilibrium, in the characterization of biological phase transitions. On the other hand, it was evidenced how the rate of entropy production represents a physical quantity to evaluate the complexity and robustness of cancer.

Quantum Computers are provisioned as very high performance computers using quantum mechanical aspects for information processing. Quantum Information Theory and Quantum Computing topics are popular topics in academia aiming the construction of theoretical background of Quantum Computers. The information processing units for Quantum Computers are defined as qubits but for some problems three level (trinary) systems may be applied as well. We call these three level systems as qutrits. The scope of this work is the analysis of well-defined entanglement measures Negativity and Relative Entropy of Entanglement (REE) for two qutrit (3- level/trinary) quantum systems. In this manner, for randomly generated 1000 two qutrit and 1000 two qubit states the mentioned measures are calculated and these values are compared. These comparisons are analyzed and for quantum state ordering problem, some interesting results are reported.

The high entropy alloy (HEA) of equiatomic composition CrNiFeCoMn and with FCC crystal structure was additively manufactured with a selective laser melting (SLM) process starting from mechanically alloyed powders. The as produced alloy shows finenitride and  phase pre-cipitates, which are Cr-rich and stable up to about 900 K. The precipitates increase in number and dimensions after long-period annealing at 900-1300 K, with a change in the HEA mechanical properties. Higher aging temperatures in furnace, above 1300 K, turn the alloy in a single FCC structure, with disappearance of the nitrate and  phase precipitates inside the grains and at the grain boundaries, but with still a presence of a finer Cr-rich nitride precipitation phase. These re-sults suggest that the as-produced HEA is a supersatured solid solution at low and intermediate temperature with nitrides and  nanostructures.

We review our theory of interdependence applied to autonomous human-machine teams, with which we have made several generalizations based on theory that have led to new discoveries, compared to social science which is struggling to break free of its validation crisis, but also has no generalizations to new discoveries with human teams, let alone to human-machine teams. In this invited article, based around the stability of a team, of our discoveries, we review the uncertainty between a team's structure and its performance, our first finding. We generalize that finding to deception, vulnerability, innovation and fittedness. From there, our next generalization is to the quantum likeness of interdependence and quantum mechanics; we move on to Shannon holes, knowledge, and conclude with the value of debate and the need for boundaries to contain debate, to reduce interference, and to protect states of interdependence. After the introduction, we extend our model in Section 2 to energy and time, and we close with a brief review of innovation and future plans.

We investigate some of the fundamental features of the interaction of mixed kaleidoscope states, namely, particular statistical mixtures of coherent states, with two-level atoms in the Jaynes-Cummings model framework. We begin our analysis by calculating the von Neumann entropy of the field which is determined with help of the virtual atom method. Oscillations appear in this entropy that indicate a state of purity greater than the initial state, {it i.e.}, a purification of the initial state is achieved. In this oscillatory region, we obtain the field Wigner function that resembles Schrodinger's cats.

One of the intriguing recent results in the field of high-entropy alloys is the discovery of single-phase equiatomic multi-component Laves intermetallics. However, there is no clear understanding that a combination of chemical elements will form such high-entropy compounds. Here we contribute to understanding this issue by modifying the composition of duodenary TiZrHfNbVCrMoMnFeCoNiAl (12x) alloy in which we recently reported the fabrication of hexagonal C14 Laves phase. We consider three alloys based on 12x: 7x=12x-VCrMoMnFe, 12x+Sc, 12x+Be and observe that all of them crystalize with the formation of C14 Laves phase as a dominant structure. We report that 12x+Be alloy reveals single-phase C14 structure with very high concentration of structural defects and ultra-fine dendritic microstructure with almost homogenous distribution of the constituted elements over the alloy matrix. The 7x and 12x+Sc alloys contain C14 as a main phase and unknown impurity phases. To characterize the materials, we examine their heat capacity, electrical conductivity and magnetic properties. The measurements reveal that the Laves phases are Curie-Weiss paramagnets, which demonstrate metallic conduction; 7x and 12x alloys also reveal a pronounced Kondo-like anomaly. Analysis of experimental data as well as ab initio calculations suggests that chemical complexity and compositional disorder cause strong s-d band scattering and thus the rather high density of d-states in the conduction band. Analysis of the results suggests that the mechanism of Laves phase formation in multicomponent multi-principal element metallic alloys is may be the same as in polydisperse hardspheres mixtures. Another important conclusion is that the configurational entropy is a negligible factor in the stabilization of multi-element Laves phases.

In this work, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced bilattice of four vertices. We use the logarithmic function of the Shannon entropy H_(s) to construct the paraconsistent equations and thus adapt a probabilistic model for representations in quantum physics. Through analyses of the interlaced bilattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, quantum entanglement, wave functions, and equations that determine the energy levels of the layers of an atom. At the end of this article, we use the hydrogen atom as a basis of the representation of the PAL2v model, where the values of the energy levels in six orbital layers are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.

Despite their obvious differences, biological systems at different scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are usually obscured by the parcelled terminology employed by various scientific sub-disciplines. To explore these commonalities, this papers a comparative study of diverse applications of the maximum entropy principle, ranging from amino acids up to societies. By presenting these studies under a common language, this paper establishes a unified view over seemingly highly heterogeneous biological scenarios.

Living beings are composite thermodynamic systems in non-equilibrium conditions. Within this context, there are a number of thermodynamic potential differences (forces) between them and the surroundings, as well as internally. These forces lead to flows, which, ultimately, are essential to life itself. Living beings are under the pressures of natural selection, thus are biological flows as well. At the same time, the maintenance of homeostatic conditions, the tenet of physiology, demands regulation of these flows by control of variables. However, due to the very nature of these systems, regulation of flows and control of variables become entangled in closed loops. Therefore, the search for adaptation in flows takes a different path than the search for adaptation in morphological traits. Being at the roots of transfer processes, thermodynamic criteria turn out to be as natural physical candidates. Likewise, being at the roots of physiology, control turns out to be as a natural biological candidate in that path. Here we show how to combine entropy generation, with respect to a generalized process, and control of parameters (in such a generalized process) in order to create a criterium of optimal ways to regulate changes in generalized flows.

In this paper, we revisit the q-states clock model for small systems. We present results for the thermodynamics of the q-states clock model from $q=2$ to $q=20$ for small square lattices $L \times L$, with L ranging from $L=3$ to $L=64$ with free-boundary conditions. Energy, specific heat, entropy and magnetization are measured. We found that the Berezinskii-Kosterlitz-Thouless (BKT)-like transition appears for $q>5$ regardless of lattice size, while the transition at $q=5$ is lost for $L<10$; for $q\leq 4$ the BKT transition is never present. We report the phase diagram in terms of $q$ showing the transition from the ferromagnetic (FM) to the paramagnetic (PM) phases at a critical temperature T$_1$ for small systems which turns into a transition from the FM to the BKT phase for larger systems, while a second phase transition between the BKT and the PM phases occurs at T$_2$. We also show that the magnetic phases are well characterized by the two dimensional (2D) distribution of the magnetization values. We make use of this opportunity to do an information theory analysis of the time series obtained from the Monte Carlo simulations. In particular, we calculate the phenomenological mutability and diversity functions. Diversity characterizes the phase transitions, but the phases are less detectable as $q$ increases. Free boundary conditions are used to better mimic the reality of small systems (far from any thermodynamic limit). The role of size is discussed.

The entropy of a system gives a powerful insight into its microscopic degrees of freedom, however standard experimental ways of measuring entropy through heat capacity are hard to apply to nanoscale systems, as they require the measurement of increasingly small amounts of heat. Two alternative entropy measurement methods have been recently proposed for nanodevices: through charge balance measurements and transport properties. We describe a self-consistent thermodynamic framework for treating few-electron nanodevices which incorporates both existing entropy measurement methods, whilst highlighting several ongoing misconceptions. We show that both methods can be described as special cases of a more general relation and prove its applicability in systems with complex microscopic dynamics – those with many excited states of various degeneracies.

Background: Early detection of atrial fibrillation (AF) is essential to prevent stroke and other cardiac and embolic complications. We compared the diagnostic properties for AF detection of the percentage of successive RR interval differences greater than or equal to 30 ms or 3.25% of the previous RR interval (pRR30 and pRR3.25%, respectively), and asymmetric entropy descriptors of RR intervals. Previously, both pRR30 and pRR3.25% outperformed many other heart rate variability (HRV) parameters in distinguishing AF from sinus rhythm (SR) in 60-second electrocardiograms (ECGs). Methods: The 60-s segments with RR intervals were extracted from the publicly available Physionet Long-Term Atrial Fibrillation Database (84 recording, 24-hour Holter ECG). There were 31753 60-s segments of AF and 32073 60-s segments of SR. The diagnostic properties of all parameters were analysed with the receiver operator curve analysis, confusion matrix and logistic regression. The best model with pRR30, pRR3.25% and total entropic features (H) had the largest area under the curve (AUC) – 0.98 compared to 0.959 for pRR30 - and 0.972 for pRR3.25%. However, the differences in AUC between pRR30, pRR3.25% alone and the combined model were negligible from a practical point of view. Moreover, combining pRR30, pRR3.25% with H significantly increased the number of false-negative cases by more than threefold. Conclusions: Asymmetric entropy has some potential in differentiating AF from SR in the 60-s RR interval time series, but the addition of these parameters does not seem to make a relevant difference compared to pRR30 and especially pRR3.25%.

Entropy as a mathematical concept is the first of its own kind, and second to none. Barely one or two papers in literature have investigated fractal dimensions of very basic entropies, such as Shannon, Tsallis, and Rényi entropic expressions. This was a thoughtful inspiration to delve into a step forward towards a unified information- theoretic fractal theory. The storytelling of this current paper starts by introducing my third entropy formula, namely Ismail’s entropy, , as a novel generalization to Shannonian entropy with a visionary link to both long- and short-range interactions, (LRIs), (SRIs) respectively. Clearly, this would generate a fourfold unification with statistical mechanics as well as contemporary physics. Hence, this adds more credibility and weight for this study. The fractal dimension of , is identified in this paper. As an essential part of this work, it was influential to spotlight the importance of fractal geometry to space industry as well as education, which is crucial to develop our societies. Thus, some potential fractal applications to CubeSat Technologies and Education are highlighted. So, will the deep search for more ground-breaking research has come to an end. Certainly, not. This was another inspiration to propose new open problems to widen research gates to the scientific community for more research pathways. Consequently, the paper ends with closing remarks combined with some challenging open problems and the next phase of research.

One of the most prevalent brain diseases, epilepsy is characterized by recurring seizures that happen quite frequently. During seizures, a patient suffers uncontrollable muscle contractions that cause loss of motion and balance, which could lead to harm or even death. Establishing an automatic method for warning patients about impending seizures requires extensive research. It is possible to anticipate seizures by analyzing the Electroencephalogram (EEG) signal from the scalp region of the human brain. Time domain-based features such as Hurst exponent (Hur), Tsallis Entropy (TsEn), improved permutation entropy (impe), and amplitude-aware permutation entropy (AAPE) were extracted from EEG signals. In order to diagnose epileptic seizure children from normal children automatically, this study conducted two sessions, in the first session, the extracted features from the EEG dataset were classified using three machine learning (ML)-based models including support vector machine (SVM), K nearest neighbor (KNN), or decision tree (DT), while in the second session, the dataset was classified using three deep learning (DL)-based recurrent neural network (RNN) classifiers including a gated recurrent unit (GRU), long short-term memory (LSTM), and bidirectional (BiLSTM). The EEG dataset obtained from the Neurology Clinic at the Ibn-Rushd Training Hospital. In this regard, detailed explanations and research from the time domain and entropy characteristics show that using GRU, LSTM, and BiLSTM RNN deep learning classifiers on the All−time−entropy fusion feature improves the final classification results.

Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and in the finance industry. In a Boolean model, the truth state of a variable is either 0 or 1 at a given time. Despite its apparent simplicity, Boolean networks are surprisingly relevant in many areas of application such as in bioinformatics to model gene expressions and interactions. In the latter case, a gene is either ``on" or ``off" depending on its expression level. Despite the promising utility of Boolean modeling, in most practical applications the Boolean network is not known. Automated learning of a Boolean network and Boolean functions, from data, is a challenging task due in part to the large number of unknowns (including both the structure of the network and the functions) to be estimated, for which a brute force approach would be exponentially complex. In this paper we develop a new information theoretic methodology that we show to be significantly more efficient than previous approaches. Building on the recently developed optimal causation entropy principle (oCSE), that we proved can correctly infer networks distinguishing between direct versus indirect connections, we develop here an efficient algorithm that furthermore infers a Boolean network (including both its structure and function) based on data observed from the evolving states at nodes. We call this new inference method, Boolean optimal causation entropy (BoCSE), which we will show that our method is both computationally efficient and also resilient to noise. Furthermore, it allows for selection of a set of features that best explains the process, a statement that can be described as a networked Boolean function reduced order model. We highlight our method to the feature selection in several real-world examples: (1) diagnosis of urinary diseases, (2) Cardiac SPECT diagnosis, (3) informative positions in the game Tic-Tac-Toe, and (4) risk causality analysis of loans in default status. Our proposed method is effective and efficient in all examples.

The Maximum Entropy Theory of Ecology, or METE, is a theoretical framework of macroecology that makes a variety of realistic ecological predictions about how species richness, abundance of species, metabolic rate distributions, and spatial aggregation of species interrelate in a given region. In the METE framework, "ecological state variables" (representing total area, total species richness, total abundance, and total metabolic energy) describe macroecological properties of an ecosystem. METE incorporates these state variables into constraints on underlying probability distributions. The method of Lagrange multipliers and maximization of information entropy (MaxEnt) lead to predicted functional forms of distributions of interest. We demonstrate how information entropy is maximized for the general case of a distribution, which has empirical information that provides constraints on the overall predictions. We then show how METE’s two core functions are derived. These functions, called the "Spatial Structure Function" and the "Ecosystem Structure Function" are the core pieces of the theory, from which all the predictions of METE follow (including the Species Area Distribution, the Species Abundance Distribution, and various metabolic distributions). Primarily, we consider the discrete distributions predicted by METE.We also explore the parameter space defined by the METE’s state variables and Lagrange multipliers. We aim to provide a comprehensive resource for ecologists who want to understand the derivations and assumptions of basic mathematical structure of METE.

The subject of this paper is to analyse the Math Principia of Economic 3D Black Holes in Roegenian economics. This idea is totally new in the related literature, excepting our papers. In details, we study two special problems: (i) math origin of economic 3D black holes, (ii) entropy and internal political stability depending on national income and the total investment, for economic RN 3D black hole. To solve these problems, it was necessary to jump from macroeconomic side to microeconomic side (a substantial approach so different), to complete the thermodynamics-economics dictionary with new entities, to introduce the flow between two macroeconomic systems, to study the Schwarzschild type metric properties on an economic 4D system, together with Rindler coordinates, Einstein 4D PDEs, and economic RN 3D black hole. In addition, we introduce some economic Ricci type flows or waves, for further research.

The heat and matter transfer during glucose catabolism in living systems and their relation with entropy production are a challenging subject of the classical thermodynamics applied to biology. In this respect, an analogy between mechanics and thermodynamics has been performed via the definition of the entropy density acceleration expressed by the time derivative of the rate of entropy density and related to heat and matter transfer in minimum living systems. Cells are regarded as open thermodynamic systems that exchange heat and matter resulting from irreversible processes with the intercellular environment. Prigogine’s minimum energy dissipation principle is reformulated using the notion of entropy density acceleration applied to glucose catabolism. It is shown that, for out-of-equilibrium states, the calculated entropy density acceleration is finite and negative and approaches as a function of time a zero value at global thermodynamic equilibrium for heat and matter transfer independently of the cell type and the metabolic pathway. These results could be important for a deeper understanding of entropy generation and its correlation with heat transfer in cell biology with special regard to glucose catabolism representing the prototype of irreversible reactions and a crucial metabolic pathway in stem cells and cancer stem cells.

In the clinical electrophysiologic practice, the reading and comparing electroencephalographic (EEG) recordings some times is insufficient and take to much time. That is why in the last years it has begun to introduce new methods of EEG analysis, that give a better and faster understanding of the EEG dynamics and allow a rapid intervention in the patient's treatment. Tools coming from the information theory or nonlinear system as an entropy and complexity have been shown to be a very good alternative to address this problem. In this work we introduce a novel method -the permutation Lempel-ziv complexity vs permutation entropy map. This method was applied to EEG of two patients with specific diagnosed pathologies during respective follow up processes of pharmacological changes in order to detect changes that are not evident with the usual inspection method. Our results show that the proposed method are useful for observing an evolutionary retrospective clinical effects of pharmacological interventions in both patients, and from these, to follow the clinical response to the proposed treatment.

The efficient generation of high-quality random numbers is essential in the operation of cryptographic modules. The quality of a random number generator is evaluated by the min-entropy of its entropy source. Typical method used to achieve high min-entropy of the output sequence is an entropy accumulation based on a hash function. This is grounded in the famous Leftover Hash Lemma which guarantees a lower bound on the min-entropy of the output sequence. However, the hash function based entropy accumulation has slow speed in general. For a practical perspective we need a new efficient entropy accumulation with the theoretical background for the min-entropy of the output sequence. In this work, we obtain the theoretical bound for the min-entropy of the output random sequence through the very efficient entropy accumulation using only bitwise XOR operations, where the input sequences from the entropy source are independent. Moreover we examine our theoretical results by applying to the quantum random number generator that uses dark noise arising from image sensor pixels as its entropy source.

The Reactive Spark Plasma Sintering (R-SPS) method is compared in this work with the two-steps SHS-SPS route, based on combination of the Self-propagating High-temperature Synthesis (SHS) with the SPS process, for the fabrication of dense (Hf0.2Mo0.2Ti0.2Ta0.2Nb0.2)B2-SiC and (Hf0.2Mo0.2Ti0.2Ta0.2Zr0.2)B2-SiC ceramics. A multiphasic and inhomogeneous product, containing various borides, is obtained at 2000°C/20min by R-SPS, from transition metals, B4C and Si. In contrast, if the same precursors are first reacted by SHS, and then processed by SPS under the optimized condition of 1800°C/20min, the desired ceramics are successfully attained. Both High-Entropy-Boride/SiC products display densities > 97%, uniform microstructures and contained only small amounts of residual oxides (<2.4 wt.%). The presence of SiC makes the sintering temperature milder, i.e. 150°C below to that needed by the corresponding additive-free system. Fracture toughness is also markedly improved, particularly when considering the Nb-containing system processed at 1800°C/20min, whereas KIC progressively decreases (from 7.35 to 5.36 MPa m1/2) as the SPS conditions become more severe. SiC addition is found to inhibit the volatilization of metal oxides like MoO3 formed during oxidation experiments, thus avoiding mass loss in the ceramics. The benefits above also likely take advantage of the fact that the two composite constituents are synthesized in parallel, according to the SHS-SPS approach, rather than being produced separately and combined subsequently, so that strong interfaces between them are formed.

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

Two well-known drawbacks in fuzzy clustering are the requirement of assign in advance the number of clusters and random initialization of cluster centers.; the quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of FCM using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.

This paper presents a novel approach for the recognition of multiple sclerosis (MS) using wavelet entropy and a Particle Swarm Optimization (PSO)-based neural network. MS is a complex neurological disorder with diverse clinical manifestations, often challenging to diagnose accurately. In this study, we leverage wavelet entropy (WE) as a feature extraction method to capture intricate patterns within brain imaging data. These extracted features are then employed to train a neural network model optimized through PSO to enhance classification accuracy. Experimental results on a dataset comprising MS and healthy control subjects demonstrate the effectiveness of our proposed approach, viz., WE-PSONN, which achieves a sensitivity of 91.95±1.15, a specificity of 92.36±0.88, a precision of 92.28±0.88, an accuracy of 92.16±0.90. The combination of advanced signal processing techniques and machine learning optimization holds promise for improving the early diagnosis and management of MS, offering potential benefits to both patients and healthcare providers.

Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator (RNG). At the same time, it directly determines the extraction ratio of true randomness from the raw data, in other words, it obviously affects quantum random bits generating rate. In this work, we commit to enhancing quantum entropy content in the vacuum noise based quantum RNG. We have taken into account main factors in this proposal to establish the theoretical model of quantum entropy content, including the effects of classical noise, the optimum dynamical analog-digital convertor (ADC) range, the local gain and the electronic gain of the homodyne system. We demonstrate that by amplifying the vacuum quantum noise, abundant quantum entropy is extractable in the step of post-processing even classical noise excursion, which may be deliberately induced by an eavesdropper, is large. Based on the discussion and the fact that the bandwidth of quantum vacuum noise is infinite, we propose large dynamical range and moderate TIA gain to pursue higher local oscillator (LO) amplification of vacuum quadrature and broader detection bandwidth in homodyne system. High true randomness extraction ratio together with high sampling rate is attainable. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the laser power of the LO when classical noise excursions of the raw data is obvious.

We explored the dynamics of the two interacting information systems. We show that for the Markovian marginal systems the driving force for information dynamics is determined by both the information landscape and information flux. While the information landscape can be used to construct the driving force to describe the equilibrium time reversible information system dynamics, the information flux can be used to describe the nonequilibrium time-irreversible behaviours of the information system dynamics. The information flux explicitly breaks the detailed balance and is a direct measure of the degree of the nonequilibriumness or time irreversibility. We further demonstrate that the mutual information rate between the two subsystems can be decomposed into the equilibrium time-reversible and nonequilibrium time-irreversible parts respectively. This decomposition of the mutual information rate (MIR) corresponds to the information landscape-flux decomposition explicitly when the two subsystems behave as Markov chains. Finally, we uncover the intimate relationship between the nonequilibrium thermodynamics in terms of the entropy production rates and the time-irreversible part of the mutual information rate. We found that this relationship and MIR decomposition still hold for the more general stationary and ergodic cases. We demonstrate the above features with two examples of the bivariate Markov chains.

We consider open non-twist Hamiltonian systems represented by an area-preserving two-dimensional map describing incompressible planar flows in the reference frame of a propagating wave, and possessing exits through which map orbits can escape. The corresponding escape basins have a fractal nature that can be revealed by the so-called basin entropy, a novel concept developed to quantify final-state uncertainty in dynamical systems. Since the map considered violates locally the twist condition, there is a shearless barrier that prevents global chaotic transport. In this paper we show that it is possible to determine the shearless barrier breakup by considering the variation of the escape basin entropy with a tunable parameter.

Abstract: The second part of the paper develops the approach, suggested in the Entropy 2020, 22(1), 11; https://doi.org/10.3390/e22010011 , which relates ordering in physical systems to their symmetrizing. Entropy is frequently interpreted as a quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and “disorder” are vague and subjective to a much extent. This leads to numerous misinterpretations of entropy. We propose to see the disorder as an absence of symmetry and to identify “ordering” with symmetrizing of a physical system; in other words, introducing the elements of symmetry into an initially disordered physical system. We explore the initially disordered system of elementary magnets exerted to the external magnetic field H ⃗. Imposing symmetry restrictions diminishes the entropy of the system and decreases its temperature. The general case of the system of elementary magnets demonstrating the j-fold symmetry is treated. The interrelation T_j=T/j takes place, where T and T_j are the temperatures of non-symmetrized and j-fold-symmetrized systems of the magnets correspondingly.

Confidence interval of is an interval corresponding to a specified confidence and including the true value. It can be used to describe the precision of a statistical quantity and quantify its uncertainty. Although the principle of maximum entropy (POME) has been used for a variety of applications in hydrology, the confidence intervals of the POME quantile estimators have not been available. In this study, the calculation formulas of asymptotic variances and confidence intervals of quantiles based on POME for Gamma, Pearson type 3 (P3) and Extreme value type 1 (EV1) distributions were derived. Monte Carlo Simulation experiments were performed to evaluate the performance of derived formulas for finite samples. Using four data sets for annual precipitation at the Weihe River basin in China, the derived formulas were applied for calculating the variances and confidence intervals of precipitation quantiles for different return periods and the results were compared with those of the methods of moments (MOM) and of maximum likelihood (ML) method. It is shown that POME yields the smallest standard errors and the narrowest confidence intervals of quantile estimators among the three methods, and can reduce the uncertainty of quantile estimators

This study concerns calculation and comparison of Fe, Co, Ni and Cu deposition rates in tungsten codeposition process based on electrodeposition of numerous tungsten alloys. 8 different tungsten alloys containing from 2 to 5 metals were electrodeposited in constant conditions in order to compare exact reduction rates. Calculated rates enabled control of the alloy composition precise enough to obtain a high-entropy WFeCoNiCu alloy with well-balanced composition. Introduction of copper to form the quinternary alloy was found to catalyze the whole process, increasing deposition rates of all components of the high-entropy alloy.

The entropy of the partition generated by an n-tone music scale is proposed to quantify its regularity. The normalized entropy relative to a regular partition, and its complementary, here referred to as the bias, allow to analyze various conditions of similarity between an arbitrary scale and a regular scale. Interesting particular cases are scales having limited bias because their tones are distributed along interval fractions of a regular partition. The most typical case in music concerns partitions associated with well-formed scales generated by a single tone h. These scales are maximal even sets that combine two elementary intervals. Then, the normalized entropy depends on the number of tones as well as the relative size of both elementary intervals. When well-formed scales are refined, several nested families stand out with increasing regularity. It is proven that a scale of minimal bias, i.e. with less bias than those with fewer tones, is always a best rational approximation of log2h.

The aim of this articles is to investigate the entropy optimization in unsteady MHD flow Darcy-Forchheimer nanofluids towards a stretchable sheet. The surface we tend to think about is porous and stretchy under acceleration. Flow occurs due to the stretching of the surface. Four distinct types of aqueous nanostructures are taken in this examination where copper oxide ( ), copper ( ), titanium dioxide ( ) and aluminum oxide ( ) are the nanoparticles. Irreversibility analysis are discussed through second law of thermodynamics. The expression of energy is mathematically designed and discussed according to heat generation / absorption, dissipation, thermal radiation, and joule heating. The nonlinear PDE (partial differential conditions) is first changed to ODE (normal differential conditions) through appropriate similarity variables. Here we used the numerically embedded solution technique to develop a numerical result for the obtained nonlinear flow expression. Influence of various flow parameter velocity temperature distribution and entropy generation are discussed. Reduction occurs in velocity profile for larger porosity and magnetic parameters. An enhancement in entropy generation and temperature distribution is seen for Brinkman number. An opposite effect is noticed in velocity and temperature through solid volume friction.

Microcrystalline and near nanocrystalline AlCrFeCoNi high-entropy alloy (HEA) coatings were applied on Inconel 718 superalloy using air plasma spraying (APS) process. High-temperature oxidation behavior of the microcrystalline and near nanocrystalline AlCrFeCoNi HEA coated superalloy were examined at 110°C under the air atmosphere for 50 cycles under cyclic heating and cooling (1 h for each cycle). The oxidation kinetics of both nanocrystalline and microcrystalline coated superalloy was accordingly analyzed by weight change measurement. It was noticed that the uncoated and coated followed the parabolic rate law of the oxidation. X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), energy dispersive X-ray analysis (EDS), and elemental mapping techniques were used to analyze the oxidized coated and uncoated samples. In the HEA coated superalloy, Fe, Ni, Co, and Al were oxidized in the inter-splat region, whereas the splats which consist mainly of Ni and Cr remained unoxidized. Because of the formation of compact and adhesive thin NiO, CoO oxides, and spinels together with the Al2O3 oxide scale on the surface of the coating during oxidation, the developed nanocrystalline HEA coating shows better oxidation resistance than the microcrystalline HEA coating.

Modulation of the amplitude of high-frequency cortical field activity locked to changes in phase of a slower brain rhythm is known as phase-amplitude coupling (PAC). The study of this phenomenon has been gaining traction in neuroscience because of several reports on its appearance in normal and pathological brain processes in humans as well as across different mammalian species. This has led to the suggestion that PAC may be an intrinsic brain process that facilitates brain inter-area communication across different spatiotemporal scales. Several methods have been proposed to measure the PAC process, but few of these enable detailed study of its time course. It appears that no studies have reported details of PAC dynamics including its possible directional delay characteristics. Here, we study and characterize the use of a novel information theoretic measure that may address this limitation: local transfer entropy. We use both simulated and actual intracranial electroencephalographic data, and in both cases we observe initial indications that local transfer entropy can be used to detect the onset and offset of modulation process periods revealed by mutual information phase-amplitude coupling (MIPAC). We review our results in the context of current theories about PAC in brain electrical activity, and discuss technical issues that must be addressed to see local transfer entropy more widely applied to PAC analysis.

Conceiving vacuum energy as gravitational particles subject to Heisenberg’s energy-time uncertainty, modelled as dipoles in a fluidal space at thermodynamic equilibrium, and interpreting the Bekenstein-Hawking entropy as the effective amount of spins of those dipoles enclosed within the event horizon of the universe, allows the calculation of Milgrom’s acceleration constant. The result is a quantum mechanical interpretation of gravity, and dark matter in particular.

Ultra-high temperature oxidation-resistant alloys (UTORAs) have received a lot of attention due to the increased research demand for deep space exploration around the world. But UTORAs have the disadvantages of easy oxidation and chalking. So, in this study, a UTORA was prepared by hot-press sintering on VZrHfNbTa (HEA) substrate coated with hafnium. The bonding mechanism, resistance to high-temperature oxidation, and hardness of the sample tests were carried out. The results show that zirconium in the matrix will diffuse into the hafnium coating during the high-temperature sintering process and form the HfZr alloy transition layer, the coating thickness of the composite is about 120 μm, and the diffusion distance of zirconium in the hafnium coating is about 60 μm, this transition layer chemically combines the hafnium coating and the HEA substrate into a monolithic alloy composite. The results of high-temperature oxidation experiments show that the oxidation degree of the hafnium-coated VZrHfNbTa composite material was significantly lower than that of the VZrHfNbTa HEA after oxidation in air at 1600 °C for 5 h. The weight gain of the coated sample after oxidation is 56.56 mg/cm2, which was only 57.7 % compared to the weight gain of the uncoated sample (98.09 mg/cm2 for uncoated), and the surface of the uncoated HEA showed obvious dents, oxidation, and pulverization occurred on the surface and interior of the sample. In contrast, the coated composite alloy sample mainly underwent surface oxidation sintering to form a dense HfO2 protective layer, and the internal oxidation of the hafnium-coated VZrHfNbTa composite alloy was significantly lower than that of the uncoated VZrHfNbTa HEA.

We consider the quantum thermodynamic origin of the gravitational force of matter by applying the spacetime entanglement entropy and the Unruh effect originating from vacuum quantum fluctuations. By analyzing both the local thermal equilibrium and quasi-static processes of a system, we may get both the magnitude and direction of Newton's gravitational force in our theoretical model. Our work shows the possibility that the elusive Unruh effect has already shown its manifestation through gravitational force.

Epilepsy is a common neurological condition, typically diagnosed using Electroencephalogram (EEG). Large scale EEG datasets have recently been made publicly available, allowing the use of advanced Machine Learning (ML) algorithms to analyze EEG patterns associated with epilepsy. While most existing studies focus on identifying seizures in the EEG, few have tried to identify preictal EEG segments. Identifying preictal EEG segments are not only useful in developing early warning systems but also helps inform the course of treatment for the patient. In this study, we propose to represent EEG segments as images, instead of time-series data, and identify preictal EEG segments using a preexisting ML algorithm (YOLOv8) designed for image processing. Multiplexed images (containing the original EEG signal represented on a 2D grid, kurtosis, and spectral entropy) achieve the best accuracy of 95.75% on the dataset while images just containing the EEG signal result in an accuracy of 91.25%. Using only spectrograms, generated from the original EEG signal, results in an accuracy of 90.15%.

The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is derived both by tracing out the environment from a bosonic eigenstate of the union of environment and system of interest (the empirical approach) and by tracing out the environment from the mixed state of the union of environment and system of interest (the Bayesian approach). In the thermodynamic limit, the two coincide and are equal to the multinomial distribution. Furthermore, the paper proposes to identify the physical entropy of the bosonic system with the Shannon entropy of the occupancy numbers, fixing certain contradictions that arise in the classical analysis of thermodynamic entropy. Finally, by leveraging an information-theoretic inequality between the entropy of the multinomial distribution and the entropy of the multivariate hypergeometric distribution, Bayesianism of information theory and empiricism of statistical mechanics are integrated into a common ''infomechanical'' framework.

Properties of the Voronoi tessellations arising from the random 2D distribution points are reported. We applied the procedure of dividing the sides of Voronoi cells into equal or random parts to Voronoi diagrams generated by a set of randomly placed on the plane points. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude, that by applying even a simple set of rules to a random set of seeds we introduce order into an initially disordered system. At the same time, the Voronoi entropy showed a tendency to values typical for completely random patterns and did not distinguish the short-range ordering. The Voronoi entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase of the number of the iteration steps. Voronoi entropy grew, with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Voronoi entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Voronoi entropy.

High-entropy alloys (HEAs) are of great interest in the field of materials science and engineering. Unlike conventional alloys, which contain a maximum of two base metals, this new category of materials consists of multi-principle elements and the possible number of alloy compositions, in case of HEAs, is outstandingly higher than that for conventional alloys. Here, a review on the high-entropy alloys, has been provided, on the issue whether the earliest definition of High- Entropy alloys, proposed in 2004^{[2, 4]}, is consistent with one of the four-component equiatomic Compositionally complex alloys exhibiting a “High-entropy” effect.

We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data on the example of several images, and discuss further possible utilizations in other fields of data processing.

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of both observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

With the great development of intelligent transportation systems (ITS), travel time prediction has attracted the attentions of many researchers and a large number of prediction methods have been developed. However, as an unavoidable topic, the predictability of travel time series is the basic premise for travel time prediction has received less attention than the methodology. Based on the analysis of the complexity of travel time series, this paper defines travel time predictability to express the probability of correct travel time prediction and proposes an entropy-based method to measure the upper bound of travel time predictability. Multiscale entropy is employed to quantify the complexity of travel time series, and the relationships between entropy and the upper bound of travel time predictability are presented. Empirical studies are made with vehicle trajectory data in an express road section. The effectiveness of time scales, tolerance, and series length to entropy and travel time predictability are analysis, and some valuable suggestions about the accuracy of travel time predictability are discussed. Finally, the comparisons between travel time predictability and actual prediction results from two prediction models, ARIMA and BPNN, are conducted. Experimental results demonstrate the validity and reliability of the proposed travel time predictability.

A new utilization of entropy in the context of buckling is presented. The novel concept connecting strain energy and entropy for a pin-ended strut is derived. This concept rationalizes the ranking of buckling modes based on strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of buckling modes that coincide with the measurement of initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for given energy roughly decreases with the inverse square of the mode index. For practical engineering, the study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics.

The article is devoted to solving the problem of searching for universal explainable features that can remain explainable for a wide class of objects and phenomena and become an integral part of Explainable AI (XAI). The study is implemented on the example of an applied problem of early diagnostics of plant stress, using Thermal IR (TIR) and HSI, presented by 8 vegetation indices/channels. Each such index was presented by 5 statistical values. A Single-Layer-Perceptron classifier was used as the main instrument. TIR turned out to be the best of the indices in terms of efficiency in the field and sufficient to detect all 7 key days with 100% accuracy. Our study shows also that there are a number of indices, inluding NDVI, and usual color channels Red, Green, Blue, which are close to TIR possibilities in early plant stress detection with 100% accurasy or near, and can be used for wide class of plants and in different conditions their treatment. The stability of the stress classification in our study was maintained when the training set was reduced up to 10% of the dataset volume. The entropy-like feature of (max-min) for any indices/channels have determined as a leadersheep universal high-level explainable feature for the plant stress detection, which used in interaction with some of other statistical features.

Experimental methodologies for fatigue lifetime prediction are time-intensive and susceptible to environmental variables. While the cohesive zone model is popular for predicting adhesive fatigue lifetime, entropy-based methods have also shown promise. This study aims to provide an understanding of the durability characteristics of CFRP adhesive joints by incorporating an entropy damage model within the context of the finite element method (FEM), examined the effects of different adhesive layer thicknesses on SLS models. As the adhesive layer increased in thickness, DAMAGE VARIABLES initially rose and then declined, peaking at 0.3mm. This finding provides crucial understanding into the stress behavior at the resin-CFRP interface and the resin's fatigue mechanisms.

An exposition of entropy applications to highlight some potential entropic applications to artificial intelligence and knowledge transfer. Entropy is a basic idea in artificial intelligence that is applied to many different tasks, such as reinforcement learning, data compression, and decision-making. By quantifying uncertainty and information content, it helps artificial intelligence models provide predictions and decisions that are well-informed. Therefore, this paper shines on spotlighting the significance of entropy to attract the attention of artificial intelligence research community to entropy as a powerful tool to advance artificial intelligence.The significance of knowledge transfer (KT), particularly intergenerational knowledge transfer (IGT), in knowledge management is also covered in this paper. To quantify the complexity of knowledge distribution inside an organisation and assess the efficacy of knowledge transfer (KT) initiatives, the notion of knowledge entropy (KE) is presented. Additionally, the KT model—which is based on the conceptions of tacitness and information content—is introduced. It combines personalisation and codification methodologies. Future research directions are offered alongside a few difficult open problems.

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 HS were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1-6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE in the antero-posterior direction at τ 4 and τ 5, and MSE in the ML direction at τ 4 outperformed the other entropy measures in terms of discriminative ability and characterized the gait of swPD with 79%, 82%, and 78% probabilities, respectively, and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can be considered as a marker of gait variability and complexity in swPD.

True randomness is necessary for the security of any cryptographic protocol, including quantum key distribution (QKD). In QKD transceivers, randomness is supplied by one or more local private entropy sources of quantum origin, which can be either passive (e.g. a beam splitter) or active (e.g. an electronic quantum random number generator). In order to understand better the role of randomness in QKD we revisit the well-known "detector blinding" attack on BB84 QKD protocol, which utilizes strong light to achieve an undetectable and complete recovery of the secret key. We present two findings. First, we show that the detector blinding attack is in fact an attack on the receiver’s local entropy source. Second, based on this insight, we propose a modified receiver station and a statistical criterion which together enable robust detection of any bright-light attack and thus restore security.

Terrestrial vegetation dynamics are closely influenced by a multitude of factors. This study investigated the relationships between vegetation patterns and their main influencing factors. The joint entropy method was employed to evaluate the dependence between normalized difference vegetation index (NDVI) and coupled variables in the middle reaches of Hei River basin. Based on the spatial distribution of mutual information, the whole study area was divided into five sub-regions. In each sub-region, nested statistical models were applied to model the NDVI on the grid and regional scales, respectively. Results showed that the annual average NDVI increased with a rate of 0.005/a in recent 11 years. In the desert regions, the NDVI increased significantly with an increase in precipitation and temperature, and high accuracy of retrieving NDVI model was obtained by coupling precipitation and temperature, especially in sub-region I. In the oasis regions, groundwater was also an important factor driving vegetation growth, and the rise of groundwater level contributed to the growth of vegetation. However, the relationship was weaker in artificial oasis regions (sub-region III and sub-region V) due to the influence of human activities, such as irrigation. The overall correlation coefficient between the observed NDVI and modeled NDVI was observed to be 0.97. Outcomes of this study are suitable for ecosystem monitoring, especially under the realm of climate change. Further studies are necessary and should consider more factors, such as runoff and irrigation.

Single valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single valued neutrosophic cross entropy bears an asymmetrical behavior and produce an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under single valued neutrosophic set (SVNS) environment namely SN- cross entropy and prove its basic properties. Also we define weighted SN-cross entropy measure and investigate its basic properties. We develop a new multi attribute group decision making (MAGDM) strategy for ranking of the alternatives based on the proposed weighted SN-cross entropy measure between each alternative and the ideal alternative. Finally, a numerical example of MAGDM problem of investment potential is solved to show the validity and efficiency of proposed decision making strategy. We also present comparative anslysis of the obtained result with the results obtained form the existing solution strategies in the solution.

Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic hybrid sets to express incomplete information due to the presence of interval valued neutrosophic set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. In this paper we first define a new cross entropy measure under NCSs environment which we call NC- cross entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and applicability, we solve a MADM problem using the proposed strategy.

We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.

Natural time is a new time domain introduced in 2001. The analysis of time series associated with a complex system in natural time may provide useful information and may reveal properties that are usually hidden when studying the system in conventional time. In this new time domain, an entropy has been defined and complexity measures based on this entropy as well as its value under time-reversal have been introduced and found applications in various complex systems. Here, we review these applications in the electric signals that precede rupture, e.g., earthquakes, in the analysis of electrocardiograms, as well as in global atmospheric phenomena like the El Nino/La Nina Southern Oscillation.

Background: With the trend of intelligent display, the interface design of in-vehicle HUD is an expanding research field; Methods: To solve the subjectivity and uncertainty in the optimization of HUD interface design schemes, this paper proposed a hybrid scheme evaluation and optimization method based on entropy weight and VIKOR. The entropy weight method was used to reduce the subjectivity the decision-maker's weighting and obtain the objective weight of each indicator; The VIKOR method was used to obtain the best ranking of alternative schemes, and then the optimal interface design scheme was selected; Results: The evaluation of in-vehicle HUD interface design schemes were taken as an example for verification and calculation. The results showed that this method considers the subjectivity and uncertainty of the decision-making process in the optimization of design scheme, which can effectively improve the objectivity and accuracy of the evaluation results, and provide a reference for designers to optimize interface design schemes.

The SARS-CoV-2 virus, causative agent of COVID-19, is known for its genetic diversity. Virus variants of concern (VOCs) as well as variants of interest (VOIs) are classified by the World Health Organization (WHO) according to their potential risk to global health. This study seeks to enhance the identification and classification of such variants by developing a novel bioinformatics criterion centered on the virus's spike protein (SP1), a key player in host cell entry, immune response, and a mutational hotspot. To achieve this, we pioneered a unique phylogenetic algorithm which calculates EIIP-entropy as a distance measure based on the distribution of the Electron-Ion Interaction Potential (EIIP) of amino acids in SP1. This method offers a comprehensive, scalable, and rapid approach to analyze large genomic data sets and predict the impact of specific mutations. This innovative approach provides a robust tool for classifying emergent SARS-CoV-2 variants into potential VOCs or VOIs. It could significantly augment surveillance efforts and understanding of variant characteristics, while also offering potential applicability to the analysis and classification of other emerging viral pathogens and enhancing global readiness against emerging and re-emerging viral pathogens.

We report the application of a recently proposed approach for modeling biological systems using a maximum entropy production rate principle in lieu of having in vivo rate constants. The method is applied in four steps: (1) a new ODE-based optimization approach based on Marcelin’s 1910 mass action equation is used to obtain the maximum entropy distribution, (2) the predicted metabolite concentrations are compared to those generally expected from experiment using a loss function from which post-translational regulation of enzymes is inferred, (3) the system is re-optimized with the inferred regulation from which rate constants are determined from the metabolite concentrations and reaction fluxes, and finally (4) a full ODE-based, mass action simulation with rate parameters and allosteric regulation is obtained. From the last step, the power characteristics and resistance of each reaction can be determined. The method is applied to the central metabolism of Neurospora crassa and the flow of material through the three competing pathways of upper glycolysis, the non-oxidative pentose phosphate pathway, and the oxidative pentose phosphate pathway are evaluated as a function of the NADP/NADPH ratio. It is predicted that regulation of phosphofructokinase (PFK) and flow through the pentose phosphate pathway are essential for preventing an extreme level of fructose 1, 6-bisphophate accumulation. Such an extreme level of fructose 1,6-bisphophate would otherwise result in a glassy cytoplasm with limited diffusion, dramatically decreasing the entropy and energy production rate and, consequently, biological competitiveness.

Computational Fluid Dynamics (CFD) is utilized to study entropy generation for the rarefied steady state laminar 2-D flow of air-Al2O3 nanofluid in square cavity equipped with two solid fins at the hot wall. Such flows are of great importance in industrial applications, such cooling of the electronic equipment’s and nuclear reactors. In the current study, effects of Knudsen number (Kn), Rayleigh number (Ra) and the nano solid particles volume fraction (ϕ) on the entropy generation are investigated. The values of parameters considered in this work are as follows: 0≤Kn≤0.1, 〖10〗^3≤Ra≤〖10〗^6,0≤ϕ≤0.2. Length of the fins (LF) is considered to be fixed and equals to 0.5 m, whereas the location of the fins with respect to the lower wall (HF) is set to 0.25 and 0.75 m. Simulations demonstrate that there is an inverse direct effect of Kn on the entropy generation. Moreover, it is found that when Ra is less than 104, the entropy generation, due to the flow, increases as ϕ increases. In addition, the entropy generation due to the flow will decrease at Ra greater than 104 as ϕ increases. Moreover, the entropy generation due to heat will increase as both the ϕ and Ra increase. In addition, a correlation model of the total entropy generation as a function of all of the investigated parameters in this study is proposed. Finally, an optimization technique is adapted to find out the conditions at which the total entropy generation is minimized

This work probes the combined effects of magnetic field and viscous dissipation on heat field and examine the second law analysis (entropy generation) in an electrically conducting fluid under the effect of wall mass transfer over continuous stretched non-isothermal surface with variable viscosity. The viscosity of the fluid is assumed to be an inverse linear function of temperature. The governing equation for the problem are changed to dimensionless ordinary differential equations by using similarity transformation and solved numerically by using Rung Kutta and Shooting technique. Velocity, concentration and temperature distribution are obtained and used to compute the entropy generation and the Bejan number in the flow field. The effect of variable viscosity, Schmidt number, Hartman and Reynolds number on the velocity, concentration, temperature, entropy generation and Bejan number are studied and discussed.

The effect of Zr addition on the melting temperature of the CoCrFeMnNi High Entropy Alloy (HEA), known as the “Cantor’s Alloy”, is investigated, together with its microstructure, mechan-ical properties and thermo-mechanical recrystallization process. The base and Zr-modified al-loys are obtained by vacuum induction melting of mechanically pre-alloyed powders followed by recrystallization. The alloys were characterized by X-ray diffraction, scanning and transmis-sion electron microscopy, thermal analyses, mechanical spectroscopy and indentation measures. The main advantages of Zr addition are: 1) a fast vacuum induction melting (VIM) process; 2) the lower melting temperature, due to Zr eutectics formation with all the Cantor’s alloy elements; 3) the good chemical alloy homogeneity; 4) the mechanical properties improvement of recrystallized grains with a coherent structure. The crystallographic lattice of both alloys resulted to be FCC. Results demonstrate that the Zr-modified HEA presents a higher recrystallization temperature and smaller grain size after recrystallization with respect to the Cantor’s alloy, with precipita-tion of a coherent second phase which enhance the alloy hardness and strength, while maintaining a good tensile ductility.

Gait is a basic cognitive propositive action that has been shown to be altered in late stages of neurodegenerative dementias. Nevertheless, alterations are less clear in mild forms of dementia, and the potential use of gait analysis as a biomarker of initial cognitive decline has hitherto mostly been neglected. We here report the results of a study of gait kinematic time series for two groups of patients (Mild Cognitive Impairment and mild Alzheimer's disease) and a group of matched control subjects. Two metrics based on permutation patterns are considered, respectively measuring the complexity and irreversibility of the time series. Results indicate that kinematic disorganisation is present at early phases of cognitive impairment; in addition, they depict a rich scenario, in which some joint movements display an increased complexity and irreversibility, while others a marked decrease. Beyond their potential use as biomarkers, complexity and irreversibility metrics can open a new door towards the understanding of the role of the nervous system in gait, as well as its adaptation and compensatory mechanisms.

This study presents a comprehensive investigation of entropy generation during natural convection in a porous medium with Casson fluid. The governing equations, including the momentum, energy, and entropy balance equations, are solved numerically using finite element method. Through the analysis, various parameters affecting entropy generation are investigated, such as the Casson fluid parameter, Radiation, Prandtl number, and Rayleigh number. The results indicate that the Casson fluid parameter significantly influences the flow and heat transfer characteristics, while the Darcy number and Rayleigh number control the intensity of natural convection. Moreover, the Prandtl number determines the relative significance of heat transfer compared to viscous effects.

Based on a measuring system to determine levels of spatial organization in 2D polygons (homogeneous or heterogeneous partition of defined areas) lying on principles of regularity, we propose the entropy term linked to the concept of “information”, from the “information theory field”, in order to obtain an information measurement regarding a quantity of or amount of information in the architecture of complex 2D biological organizations. The term “quantity” does not refer to the amount of data (size), but to the probability of a geometrical basic pattern within a set of possible statistical configurations regarding levels of homogeneity and heterogeneity. It is this notion of information that is important in information theory, and measures of information in units of bits, what we propose to use for measuring quantities of organization in the architecture of complex geometrical systems. Two complex systems are tested, biological and non biological in order to obtain experimental results, which are verified with the evaluation criteria “entropy”. Experimental results show that the lowest levels of information and entropy, in addition with low rates of heterogeneity and high rates of homogeneity are particular features of geometrical organizations in biological systems.

Abstract: Rural digital governance is an inevitable requirement to improve the efficiency of rural governance, and is also an important means to realize the modernization of rural governance. In the context of the digital rural development strategy, the index measurement system of rural digital governance level is built around five key governance areas of "digital economy, digital ecology, digital culture, digital people's livelihood, and digital government affairs". The entropy weight Topsis model is used to measure and evaluate the level of rural digital governance in 31 provinces in China in 2021. The results show that there is a large gap in the level of digital governance in China's counties and villages, and the level of each region presents a decreasing spatial distribution from "east - middle - west". In terms of digital economy, the eastern region has a high score and good development, while the central and western regions have poor development. In terms of digital ecology, only the eastern region is higher than the national average; In terms of digital culture, only the central region is higher than the national average; In terms of digital livelihood and digital government, the central and eastern regions are slightly higher than the national average; The top three provinces in overall scores are Zhejiang, Guangdong and Jiangsu.

The performance of bearings plays a pivotal role in determining the dependability and security of rotating machinery. In intricate systems demanding exceptional reliability and safety, the ability to accurately forecast fault occurrences during operation holds profound significance. Such predictions serve as invaluable guides for crafting well-considered reliability strategies and executing maintenance practices aimed at enhancing reliability. In order to ensure the reliability of bearing operation, this article investigates the application of three advanced techniques—Maximum Correlation Kurtosis Deconvolution (MCKD), Multi-Scale Permutation Entropy (MPE), and Long Short-Term Memory (LSTM) recurrent neural networks—for the prediction of the remaining useful life (RUL) of rolling bearings. Each technique's principles, methodologies, and applications are comprehensively reviewed, offering insights into their respective strengths and limitations. Case studies and experimental evaluations are presented to assess their performance in RUL prediction. Findings reveal that MCKD enhances fault signatures, MPE captures complexity, and LSTM excels in modeling temporal patterns. The root mean square error of the prediction results is 0.007. The fusion of these techniques offers a comprehensive approach to RUL prediction, leveraging their unique attributes for more accurate and reliable predictions.

The healthy function of the vestibular system (VS) is of vital importance for individuals to carry out their daily activities independently and safely. This study carries out Tsallis entropy (TE)-based analysis on insole force sensor data in order to extract features to differentiate between healthy and VS-diseased individuals. Using a specifically developed algorithm, we detrend the acquired data to examine the fluctuation around the trend curve in order to consider the individual’s walking habit and thus increase the accuracy in diagnosis. It is observed that the TE-value increases for diseased people as an indicator of the problem of maintaining balance. As one of the main contributions of this study, in contrast to studies in the literature that focus on gait dynamics requiring extensive walking time, we directly process the instantaneous pressure values, enabling to reduce the data acquisition period significantly. The extracted feature set is then inputted into fundamental classification algorithms, with the Support-Vector-Machine (SVM) demonstrating the highest performance, achieving an average accuracy of 95%. This study constitutes a significant step of a large project aiming to identify specific VS disease together with its stage. The performance achieved in this study provides a strong motivation to further explore this topic.

Ransomware attacks have rapidly proliferated, inflicting severe financial damages on businesses and individuals. Machine learning approaches to automate ransomware detection have shown promise but grapple with challenges like limited training data. This study introduces a novel deep learning model for few-shot ransomware classification. The model employs entropy features derived directly from malware binaries coupled with a twin neural network architecture utilizing transfer learning. Tests on over 1000 samples across 11 families demonstrate a weighted F1-score of 85.8\%, surpassing existing methods. The approach mitigates biases in limited training data and preserves intricacies lost in image-based features. It exhibits precise classification capabilities even with sparse samples of new ransomware variants. The research highlights the potential of entropy-driven deep learning to equip defenses against emerging zero-day ransomware strains.

We consider the thermodynamic and stability problem of Kerr black holes arising from the nonextensive/nonadditive nature of the Bekenstein-Hawking entropy formula. Nonadditive thermodynamics is often criticized by asserting that the zeroth law cannot be compatible with nonadditive composition rules, so in this work we follow the so-called formal logarithm method to derive an additive entropy function for Kerr black holes satisfying also the zeroth law's requirement. Starting from the most general, equilibrium compatible, nonadditive entropy composition rule of Abe, we consider the simplest, non-parametric approach that is generated by the explicit nonadditive form of the Bekenstein-Hawking formula. This analysis extends our previous results on the Schwarzschild case and shows that the zeroth law compatible temperature function in the model is independent of the mass-energy parameter of the black hole. By applying the Poincaré turning point method we also study the thermodynamic stability problem in the system.

Diminished ovarian reserve can be regarded as a sentinel indicator to foreshadow severe follicular loss and, ultimately, systemic aging. The negative slope of human ovulatory fidelity begins with a robust follicular endowment which gradually declines over time. In contrast, the youthful ovarian phenotype requires the coordinated work of endothelial, granulosa, immune, perivascular, stromal and possibly germline stem cells. Such a diverse tissue matrix can, in general, be influenced by platelet (PLT)-derived factors but this has not yet been specifically confirmed in the ovary after platelet-rich plasma (PRP). How could a comparable response be validated? Here a prospective, experimental study is proposed whereby eligible patients already undergoing scheduled laparoscopy provide ovarian tissue via biopsy submitted for co-culture with autologous Ca⁺² activated PRP. Recognizing the interlocking, central roles of nuclear factor κB (NF-κB) and tumor necrosis factor-α (TNF-α), incubated samples would be assessed for these in vitro before vs. after PRP exposure, in addition to stereomicroscopy. A mathematical model is available to track NF-κB oscillations and estimate gene expression, cell development, growth, apoptosis, and key immune and inflammatory actions. Since NF-κB and TNF-α are discharged in activated PLT releasate (or react to its cargo proteins) this audit permits extraction of response markers observed post-stimulus, thus linking discrete signals to transcriptional output, cellular fitness, and ovarian cytoarchitecture. From this, a hypothesis could emerge where intraovarian PRP is found to make no direct impact on follicles, although modified ovarian field function and curtailed local entropy incidentally favor optimized oocyte competence as a secondary effect.

This paper proposes a non-extensive entropy econometric technique to predict energy efficiency at province (NUT-2) level based on imperfect knowledge of the national overall efficiency in the sectors of industry, transport, households and services. The model is applied to the polish case. As acknowledged in recent literature, non-extensive entropy model should remain a valuable device for econometric modelling even in the case of low frequency series since outputs provided by the Gibbs-Shannon entropy approach correspond to the Tsallis entropy limiting case of the Gaussian law when the Tsallis q-parameter converges to unity. Therefore, we set up a q-Tsallis-Kullback-Leibler entropy criterion function with a priori consistency moment and model data constraints, including province energy intensity (known with uncertainty), regional climate differentiation and regular conditions. The model outputs continue to conform to empirical expectations. In spite of the close to unity q-Tsallis parameter, this Tsallis related approach reflects higher stability for parameter computation in comparison with the Shannon-Gibbs entropy econometrics technique. The proposed technique can be applied in different EU countries and elsewhere for example in the context of experimental official statistics.

In recent years, the individualized demand of customers brings small batches and diversification of orders towards enterprises. The application of enabling technologies in factory, such as the Industrial Internet of Things (IIoT) and Cloud Manufacturing (CMfg), enhances the ability of customer requirement automatic elicitation and the manufacturing process control. The job shop scheduling problem with random job arrival time dramatically increases the difficulty in process management. Thus, how to collaboratively schedule the production and logistics resources in the shop floor is very challenging, and it has a fundamental and practical significance of achieving the competitiveness for an enterprise. To address this issue, the real-time model of production and logistics resources is built firstly. Then, the task entropy model is built based on the task information. Finally, the real-time self-adaption collaboration of production and logistics resources is realized. The proposed algorithm is carried out based on a practical case to evaluate its effectiveness. Experimental results show that our proposed algorithm outperforms three existing algorithms.

The continuous energy transformation processes in heating, ventilation and air conditioning systems of buildings are responsible for 36% of global final energy consumption. Tighter thermal insulation requirements for buildings have significantly reduced heat transfer losses. Unfortunately, this has little effect on energy demand for ventilation. On the basis of the First and the Second Law of Thermodynamics, the concepts of entropy and exergy are applied to the analysis of ventilation air handling unit (AHU) with a heat pump in this paper. This study aims to develop a consistent approach for this purpose, taking into account the variations of reference temperature and temperatures of working fluids. An analytical investigation on entropy generation and exergy analysis are used, when exergy is determined by calculating coenthalpies and evaluating exergy flows and their directions. The results show that each component of the AHU has its individual character of generated entropy, destroyed exergy and exergy efficiency variation. However, the evaporator of heat pump and fans have unabated quantities of exergy destruction. The exergy efficiency of AHU decreases from 45-55% to 12-15% when outdoor air temperature is within the range of –30°C…+10°C, respectively. This helps to determine conditions and components of improving the exergy efficiency of the AHU at variable real-world local climate conditions. The presented methodological approach could be used in the dynamic modelling software and contribute to a wider application of the Second Law of Thermodynamics in practice.

The logarithmic correction to Bekenshtein$-$Hawking entropy in the framework of 4D Einstein - Gauss - Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore the black hole solution with the spherically symmetric metric. The logarithmic term in the entropy has a structure similar to the entropy correction in the semi-classical Einstein equations which mimics the quantum correction to the area low. The energy emission rate of black holes and energy conditions are studied. The quasinormal modes of a test scalar field are investigated. The gravitational lensing of light around BHs was studied. We calculated the deflection angle for some model parameters.

The service conditions of underground coal mine equipment are poor, and it is difficult to accurately extract the fault characteristics of rolling bearings. In order to better improve the accuracy of fault identification of rolling bearings, a fault detection method based on multiscale permutation entropy and SOA-SVM is proposed. First, the whale optimization algorithm is used to select the modal analysis number K and the penalty factor α of the variational mode decomposition algorithm. Then, the vibration signal of rolling bearings is dissolved according to the optimized variational mode decomposition algorithm, and the multi-scale permutation entropy of the main intrinsic mode function is calculated. Finally, the feature values of the matrix are entered into the SVM algorithm optimized by the seagull optimization algorithm to obtain the classification result. The experimental results based on the published rolling bearing datasets of Western Reserve University show that the identification success rate of the proposed method can reach 98.75%. The fault detection of the rolling bearings can be completed accurately and efficiently.

Sustainable development of our society demands recycling of metallic wastes which may contain a variety of metallic impurities. Thus, it is desirable to develop a ‘universal’ structure, such as an amorphous alloy tolerating high concentrations of metallic pollutants. We performed ab initio molecular dynamics simulations to manufacture a novel multicomponent amorphous alloy of twenty elements (20e-HEAA). Analysis reveals both topological and chemical compositional short-range ordering in the obtained 20e-HEAA and formation of B-B clusters. Electronic structure calculations reveal the metallic nature of the amorphous alloy with its Fermi level falling in a valley in the density of states. Moreover, the Zn 3d and Cd 4d electrons exhibit a localized nature and thus, should be excluded from the valence electron concentration (VEC) analysis in the study of high-entropy alloys. The information obtained here is helpful to get insight into multicomponent high entropy materials, especially multicomponent high-entropy amorphous alloys as potential circular metals.

Here we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is based on two primary postulates: that small systems can be treated self-consistently by coupling them to an ensemble of similarly small systems, and that a large ensemble of small systems forms its own thermodynamic bath. We adapt this “nanothermodynamics” to investigate how a large system may subdivide into an ensemble of smaller subsystems, causing internal heterogeneity across multiple size scales. For the semi-classical ideal gas, maximum entropy favors subdividing a large system of “atoms” into an ensemble of “regions” of variable size. The mechanism of region formation could come from quantum exchange symmetry that makes atoms in each region indistinguishable, while decoherence between regions allows atoms in separate regions to be distinguishable by their distinct locations. Combining regions reduces the total entropy, as expected when distinguishable particles become indistinguishable, and as required by a theorem in quantum mechanics for sub-additive entropy. Combining large volumes of small regions gives the usual entropy of mixing for a semi-classical ideal gas, resolving Gibbs paradox without invoking quantum symmetry for atoms that may be meters apart. Other models presented here are based on Ising-like spins, which are solved analytically in one dimension. Focusing on the bonds between the Ising-like spins we find similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for fully-accurate predictions. Another result using Ising-like spins involves simulations that include a nonlinear correction to Boltzmann’s factor, which mimics the statistics of indistinguishable states by imitating the dynamics of spin exchange on intermediate lengths. These simulations exhibit 1/f-like noise at low frequencies (f), and white noise at higher f, similar to equilibrium thermal fluctuations found in many materials.

This article introduces an analytical framework that interprets individual measures of entropy-based mobility derived from mobile phone data. We explore and analyze two widely recognized entropy metrics: random entropy and uncorrelated Shannon entropy. These metrics are estimated through collective variables of human mobility, including movement trends and population density. By employing a collisional model, we establish statistical relationships between entropy measures and mobility variables. Furthermore, our research addresses three primary objectives: firstly, validating the model; secondly, exploring correlations between aggregated mobility and entropy measures in comparison to five economic indicators; and finally, demonstrating the utility of entropy measures. Specifically, we provide an effective population density estimate that offers a more realistic understanding of social interactions. This estimation takes into account both movement regularities and intensity, utilizing real-time data analysis conducted during the peak period of the Covid-19 pandemic.

Lamellar eutectic structure of Al_0.7CoCrFeNi high-entropy alloy (HEA) is emerging as a promising candidate for structural applications because of its high strength-ductility combination. The alloy consists of a fine-scale lamellar fcc+B2 microstructure with high flow stresses >1500 MPa under quasi-static conditions. The response to shear loading was not investigated so far. This is the first report on the shear deformation of an eutectic structured HEA and effect of precipitation on shear deformation. The dynamic shear response (DSR) of the eutectic HEA was examined in two microstructural conditions, with and without the presence of L1₂ precipitates. A split-Hopkinson pressure bar (SHPB) was used to compress the hat-shaped specimens to study the local DSR of the alloy. The adiabatic shear bands (ASBs) in two different microstructural conditions were characterized after deformation at dynamic strain rates. The adiabatic shear localization occurs at low strains for the high strength material, and the eutectic microstructure does not delay cracking. The width of ASBs and the extent of plastic deformation around them has been correlated with the rate of straining. Dynamic recrystallization within ASBs and profuse twinning around it was observed. Local mechanical response of individual lamellae before and after shear deformation was examined using nano-indentation.

Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.

Modern war is sudden and rapid, and once the battle starts, the demand for equipment maintenance and guarantee will show an outburst situation, which puts equipment maintenance and guarantee capability to a severe test. To accurately grasp the civil-military integration of aviation maintenance and guarantee capabilities, it is necessary to evaluate their capabilities. To this end, the evaluation indicator system is established by using the three-dimensional indicator system construction model of "maintenance task → task demand → capability demand", and the evaluation method based on intuitionistic fuzzy entropy and normal grey cloud model is proposed, using intuitionistic fuzzy entropy theory to determine the expert weights and indicator weights, and the grey cloud model theory to determine the capability evaluation level. Finally, the application process of the evaluation model is demonstrated through specific examples, and the evaluation results are analyzed to verify the effectiveness of the evaluation model.

Modern war is sudden and rapid, and once the battle starts, the demand for equipment maintenance and guarantee will show an outburst situation, which puts equipment maintenance and guarantee capability to a severe test. To accurately grasp the civil-military integration of aviation maintenance and guarantee capabilities, it is necessary to evaluate their capabilities. To this end, the evaluation indicator system is established by using the three-dimensional indicator system construction model of "maintenance task → task demand → capability demand", and the evaluation method based on intuitionistic fuzzy entropy and normal grey cloud model is proposed, using intuitionistic fuzzy entropy theory to determine the expert weights and indicator weights, and the grey cloud model theory to determine the capability evaluation level. Finally, the application process of the evaluation model is demonstrated through specific examples, and the evaluation results are analyzed to verify the effectiveness of the evaluation model.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

The calculation of the vapour pressure of organic molecules at 298.15K is presented using a commonly applicable computer algorithm based on the group-additivity method. The basic principle of this method rests on the complete breakdown of the molecules into their constituting atoms, further characterized by their immediate neighbour atoms. The group contributions are calculated by means of a fast Gauss-Seidel fitting algorithm using the experimental data of 2036 molecules from literature. A ten-fold cross-validation procedure has been carried out to test the applicability of this method, which confirmed excellent quality for the prediction of the vapour pressure, expressed in log(pa), with a cross-validated correlation coefficient Q2 of 0.9938 and a standard deviation  of 0.26. Based on these data, the molecules' standard Gibbs free energy G°vap has been calculated. Furthermore, using their enthalpies of vaporization, predicted by an analogous group-additivity approach published earlier, the standard entropy of vaporization S°vap has been determined and compared with experimental data of 1129 molecules, exhibiting excellent conformance with a correlation coefficient R2 of 0.9598, a standard error  of 8.14 J/mol/K and a medium absolute deviation of 4.68%.

Over the past decade and a half, dynamic functional imaging has revolutionized the neuroimaging field. Since 2009, it has revealed low dimensional brain connectivity measures, has identified potential common human spatial connectivity states, has tracked the transition patterns of these states, and has demonstrated meaningful alterations in these transition and spatial patterns in neurological disorders, psychiatric disorders, and over the course of development. Recently, researchers have begun to analyze this data from the perspective of dynamic system and information theory in the hopes of understanding how these dynamics support less easily quantified processes, such as information processing, cortical hierarchy, and consciousness. Consciousness, in particular, appears to be strongly linked to entropy production in the brain. Little attention has been paid to the effects of psychiatric disease on entropy production in the human brain, however. Even disorders characterized by substantial changes in conscious experience have not been widely analyzed from this perspective. We begin to rectify this by examining the complexity of subject trajectories in state space through the lens of information theory. Specifically, we identify a basis for the dynamic functional connectivity state space and track subject trajectories through this space over the course of the scan. The dynamic complexity of these trajectories is assessed along each dimension of the proposed basis space. Using these estimates, we demonstrate that schizophrenia patients display substantially simpler trajectories than demographically matched healthy controls, and that this drop in complexity concentrates along specific dimensions. We also demonstrate that entropy generation in at least one of these dimensions is linked to cognitive performance. Overall, results suggest great value in applying dynamic systems theory to problems of neuroimaging and reveal a substantial drop in the complexity of schizophrenia patients’ brain function.

The poor oxidation resistance of refractory high-entropy alloys (RHEAs) is a major obstacle for their use in high-temperature engineering applications. Anti-oxidation coating technology is an effective method for improving the oxidation resistance. In this paper, the Si-20Cr-20Fe coating was prepared on MoNbTaTiW RHEA by a fused slurry method. The microstructural evolution and compositions of the silicide coating under high-temperature oxidation environment were studied. The results show that the silicide coating could effectively prevent the oxidation of the MoNbTaTiW RHEA. The initial silicide coating had a double-layer structure; a high silicon-content layer mainly composed of MSi2 as the outer layer and a low silicon-content layer mainly contained M5Si3 as the inner layer. Under high-temperature oxidation conditions, the silicon element diffused from the silicide coating to the RHEA substrate while the oxidation of the coating occurred. After oxidation, the coating was composed of an outer oxide layer and an inner silicide layer. The silicide layer moved toward the inside of the substrate, led to the increase of its thickness. Compared with the initial silicified layer, its structure did not change significantly. The structure and compositions of the oxide layer on the outer surface strongly depended on the oxidation temperature. This paper provides a strategy for protecting RHEAs from oxidation at high-temperature environments.

Abstract: The increased penetration of renewables in distribution power systems has motivated researchers to take significant interest in local energy transactions. The major goal of Local Energy Markets (LEM) is to promote the participation of small consumers in energy transactions and providing an opportunity for transactive energy systems. Such energy transactions in LEM are considered as a bi-level optimization problem in which all agents at upper and lower levels try to maximize their profits. But typical bi-level problem is very complex as it is inherently nonlinear, discontinued and strongly NP-hard. So, this article proposes the application of hybridized Cross Entropy Covariance Matrix Adaptation Evolution Strategy (CE-CMAES) to tackle such a complex bi-level problem of LEM. The proposed CE-CMAES secured the 1st rank in Testbed-2 entitled, “Bi-level optimization of end-users’ bidding strategies in local energy markets (LM)” at international competitions on Smart Grid Problems, held at GECCO 2020 and WCCI 2020. CE method is used for global exploration of search space and CMAES is used for local exploitation as its adaptive step-size mechanism prevents its premature convergence. A practical distribution system with renewable energy penetration is considered for simulation. The comparative analysis shows that the overall cost, mean fitness and Ranking Index (R.I) obtained from CE-CMAES are superior to those obtained from the state-of-the-art participated algorithms. Wilcoxon Signed Rank Statistical test also proves that CE-CMAES is statistically different from the tested algorithms.

My innovative entropy measure, Ismail entropy, namely, (IE) is an ultimate generalization to numerous generalized entropies within the literature. The fractal dimension of IE is identified in this paper. On another applicative note, this paper offers some potential applications of fractal dimension to smart cities. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.

Primary energy consumption is one of the key drivers of global CO₂ emissions that, in turn, heavily depend on the efficiency of involved technologies. Either the improvement in technology efficiency or the expansion of non-fossil fuel consumption require large investments. The planning and financing of such investments, by policy makers or global energy firms, require, in turn, reliable measures of associated global spreads and their evolution in time. In this paper, our main contribution is the introduction of index measures for accessing global spreads (that is, measures of inequality or inhomogeneity in the statistical distribution of a related quantity of interest) of technology efficiency and CO₂ emission in primary energy consumption. These indexes are based on the Gini index, as used in economical sciences, and generalised entropy measures. Regarding primary energy sources, we consider petroleum, coal, natural gas and non-fossil fuels. Between our findings, we attest some stable relations in the evolution of global spreads of technology efficiency and CO₂ emission, and a positive relation between changes in global spreads of technology efficiency and use of non-fossil fuel.