While laminar flow heat transfer and mixing in microfluidic geometries has been investigated experimentally, as has the effect of geometry-induced turbulence in microfluidic flow (it is well documented that turbulence increases convective heat transfer in macrofluidic flow), little literature exists investigating the effect of electrokinetically-induced turbulence on heat transfer at the micro scale. Using recently observed experimental data, this work employed computational fluid dynamics coupled with electromagnetic simulations to determine if electrokinetically-forced, low-Reynolds number turbulence could be observed in a rectangular microchannel with using Newtonian fluids. Analysis of the results was done via comparison to the experimental criteria defined for turbulent flow. This work shows that, even with a simplified simulation setup, computational fluid dynamics (CFD) software can produce results comparable to experimental observations of low-Reynolds turbulence in microchannels using Newtonian fluids. In addition to comparing simulated velocities and turbulent energies to experimental data this work also presents initial data on the effects of electrokinetic forcing on microfluidic flow based on entropy generation rates.

We discuss the role of the opposing principles of order and disorder in physical and biological systems in determining stability, growth and evolution and bring forth the potential role of a cosmic ordering agency. We analyze its role in decreasing entropy by coarse-graining and hence in determining the initial low entropy state of the big bang universe. Since all physical and biological systems have either cycles of order and disorder alternating, or may have chaotic evolution with non-linear laws, the same is expected of the dynamics of the whole universe as well. The entropy of the initial state of the universe could be low because of the reduction of degrees of freedom (DoF) as one moves from physical encoding to neural encoding and then on to psychic encoding of information in a nested manner by coarse-graining. It is by such encoding that this cosmic agency enables the universe to pass through the big crunch phase and then rolls it out as the big bang universe from the initial state of low entropy.

Entropy is usually understood as the quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and “disorder” are definitely obscure. 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 initially disordered physical system. We demonstrate with the binary system of elementary magnets that introducing elements of symmetry necessarily diminishes its entropy. This is true for 1D and 2D systems of elementary magnets. Imposing symmetry does not influence the Landauer Principle valid for the addressed systems. Imposing the symmetry restrictions onto the system built of particles contained within the chamber divided by the permeable partition also diminishes its entropy.

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

In the same manner that there are several statements of the second law of thermodynamics but all of them are equivalent, it is possible that most of the entropic methods applied to the nervous system and brain in particular share a similar outcome, or essence, that helps understand some aspects of the fundamentals of basic neurodynamics. In this short review focused on certain aspects of the entropic metrics some results are examined that indicate the fundamental importance of the natural tendency towards a maximal energy distribution for healthy brain activity and thus cognition to emerge.

We present a new method for assessing the strength of fuzzy rules with respect to a dataset, based on the measures of the greatest energy and smallest entropy of a fuzzy relation. Considering a fuzzy automaton (relation) in which A is the input fuzzy set and B the output fuzzy set, the fuzzy relation R1 with greatest energy provides information about the greatest strength of the input-output and the fuzzy relation R2 with the smallest entropy provides information about uncertainty of the relationship input-output. We consider a new index of the fuzziness of the input-output based over R1 and R2. In our method this index is calculated for each pair of input and output fuzzy sets in a fuzzy rule. A threshold value is set for choosing the most relevant fuzzy rules with respect to the data.

A new approach is presented to defining the amount of information, in which information is understood as the data about a finite set as a whole, whereas the average length of an integrative code of elements serves as a measure of information. We obtain a formula for the syntropy of reflection, that is, the information that two intersecting finite sets reflect about each other. The specificities of reflection of discrete systems through the combination of their parts are considered, and it is shown that the additive syntropy and entropy of reflection are measures of structural order and chaos. Three information laws have been established: the law of conservation of the sum of chaos and order; information law of reflection; the law of conservation and transformation of information. An assessment of the structural organization and the level of development of discrete systems is presented. It is shown that various measures of information are structural characteristics of integrative codes of elements of discrete systems. The conclusion is made that, from the informational-genetic positions, the synergetic theory of information is primary in relation to the Hartley-Shannon information theory. In the appendix we consider the asymmetry of the mutual reflection of finite sets and the proportionality of arbitrary quantities.

The recently proposed and logically developed paradigm of deep genetical affinity of scientific terms "energy-entropy-information" harmonizes classical and quantum physics with general and special theories of relativity. For the first time in engineering practice, a complex vector-tensor-matrix description of gravitational, thermal and electromagnetic fields in ideal solid, liquid and gaseous media was performed analytically and without preliminary measurements. The basic set of fundamental quantum constants of the standard physical model has been computed with an extreme precision of 1/10^64, which is a natural limit arising due to elementary recursive arithmetic and elementary functional analysis in digital notation.

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.

The spatial resolution measurement limitation of the position-momentum uncertainty principle is shown to mathematically originate from the Bekenstein entropy bound and the associated second law of thermodynamics, as a special case in which a statistical thermodynamic distribution of energies is specialized to a fixed, definite probe energy equal to the average energy of that distribution. This is used in combination with the Wein displacement law to predict an ultraviolet cutoff for Planck blackbody radiation at about ⅛ of the Wein peak. A new UV photon counting experiment is proposed to test for this. A physical understanding of these results may be provided by a UV-complete, intelligible theory of general relativistic quantum mechanics in which the observation of a blackbody spectrum is simply a remote observation of Hawking radiation emitted from black hole fluctuations in the gravitational vacuum.

Fatigue in any material is a result of continuous irreversible degradation process. Traditionally, fatigue life is predicted by extrapolating experimentally curve fitted empirical models. In the current study, unified mechanics theory is used to predict fatigue life of Ti-6Al-4V under monotonic tensile, compressive and cyclic load conditions. The unified mechanics theory is used to derive constitutive model for fatigue life prediction using a three-dimensional computational model. The proposed analytical and computational models have been used to predict the low cycle fatigue life of Ti-6Al-4V alloys. It is shown that the unified mechanics theory can be used to predict fatigue life of Ti-6Al-4V alloys by using simple predictive models that are based on fundamental equation of the material, which is based on thermodynamics associated with degradation of materials.

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.

Within an Internet of Multimedia Things, the risk of disclosing streamed video content, such as arising from video surveillance, is of heightened concern. This leads to the encryption of that content. To reduce the overhead and lack of flexibility arising from full encryption of the content, a good number of selective-encryption algorithms have been proposed in the last decade. Some of them have limitations, in terms of significant delay due to computational cost, or excess memory utilization, or, despite being energy efficient, do not provide a satisfactory level of confidentiality, due to their simplicity. To address such issues, this paper presents a lightweight selective encryption scheme, in which encoder syntax elements are encrypted with the innovative EXPer (EXtended Permutation with exclusive OR). The selected syntax elements are taken from the final stage of video encoding that is during entropy coding. As a diagnostic tool, the Encryption Space Ratio measures encoding complexity of the video relative to the level of encryption so as to judge the success of the encryption process, according to entropy coder. A detailed comparative analysis of EXPer with state-of-the-art algorithms confirms that the EXPer provides significant confidentiality with a small computational cost and negligible encryption bitrate overhead. Thus, the results demonstrate that the proposed security scheme is a suitable choice for constrained devices in an Internet of Multimedia Things environment.

Uncertainty is the main source of risk of geological hazards in tunnel engineering. Uncertainty information not only affects the accuracy of evaluation results, but also affects the reliability of decision-making schemes. Therefore, it is necessary to evaluate and control the impact of uncertainty on risk. In this study, the problems in existing entropy-hazard model such as inefficient decision-making and failure of decision-making are analysed, and an improved uncertainty evaluation and control process are proposed. Then the tolerance cost, the key factor in the decision-making model, is also discussed. It is considered that the amount of change in risk value (R1) can better reflect the psychological behaviour of decision-makers. Thirdly, common attribute decision models, such as the expected utility-entropy model, are analysed, and then the viewpoint of different types of decision-making issues that require different decision methods is proposed. The well-known Allais paradox is explained by the proposed methods. Finally, the engineering application results show that the uncertainty control idea proposed here is accurate and effective. This research indicates a direction for further research into uncertainty, and risk control, issues affecting underground engineering works.

The fact that individuals are spatially close to each other in the urban environment increases the potential number of encounters between them. Thus, theoretically speaking, the probability of interaction and social intercourse among people increases as they get closer to each other spatially. This reduction in spatial distance and propensity for larger networks can offer advantages in lower communication and transaction costs. However, there is also the possibility of entropy in a single (organizational) urban subsystem, characterized by reduced spatial distances between individuals that can lead to more toxic outcomes and the possibility of generalized deconstruction in an urban system as a whole. The current paper considers, through a theoretical model and secondary data analysis, how reductions in spatial distance between individuals in urban business organizations can lead to withdrawals of energy through toxic forms of entropic citizenship behavior, and lead to the development of toxic organizations. Such toxic organizations can ‘infect’ the urban system and lead to systematic entropic urban deconstruction. Practical, implications for management of the theoretical explanatory heuristic of toxic forms of organizational entropy and toxic organizations are briefly discussed in the paper.

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

Fluctuation theorems are a class of equalities each of which links a thermodynamic path functional such as heat and work to a state function such as entropy and free energy. Jinwoo and Tanaka [L. Jinwoo and H. Tanaka, Sci. Rep. 5, 7832 (2015)] have shown that each microstate of a fluctuating system can be regarded as an ensemble (or a 'macrostate') if we consider trajectories that reach each microstate. They have revealed that local forms of entropy and free energy are true thermodynamic potentials of each microstate, encoding heat, and work, respectively, within an ensemble of paths that reach each state. Here we show that information that is characterized by the local form of mutual information between two subsystems in a heat bath is also a true thermodynamic potential of each coupled state and encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange [T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012)] by showing that the fluctuation theorem holds even within an ensemble of paths that reach a coupled state during dynamic co-evolution of two subsystems.

In this study, our primary objective was to analyze the tradeoff between accuracy and complexity in machine learning models, with a specific focus on the impact of reducing complexity and entropy on the production of landslide susceptibility maps. We aimed to investigate how simplifying the model and reducing entropy can affect the capture of complex patterns in the susceptibility maps. To achieve this, we conducted a comprehensive evaluation of various machine-learning algorithms for classification tasks. We compared the performance of these algorithms in terms of accuracy and complexity, considering both "before" and "after" scenarios of dimensionality reduction using Principal Component Analysis (PCA). Our findings revealed that reducing complexity and lowering entropy can lead to an increase in model accuracy. However, we also observed that this reduction in complexity comes at the cost of losing important complex patterns in the produced landslide susceptibility maps. By simplifying the model and reducing entropy, certain intricate relationships and uncertain patterns may be overlooked, resulting in a loss of information and potentially compromising the accuracy of the susceptibility maps. The analysis encompassed a diverse range of machine learning algorithms, including Random Forest (RF), Extra Trees (EXT), XGboost, LightGBM, Catboost, Naive Bayes (NB), K-Nearest Neighbors (KNN), Gradient Boosting Machine (GBM), and Decision Trees (DT). Each algorithm was evaluated for its strengths and limitations, considering the tradeoff between accuracy and complexity. Before dimensionality reduction, the algorithms demonstrated promising results, with RF exhibiting excellent AUC/ROC scores and average accuracy. However, computational costs were noted as a potential drawback for RF, especially when dealing with large datasets. EXT showcased robust performance and good accuracy, while XGboost demonstrated its ability to handle complex relationships within large datasets, albeit requiring careful hyperparameter tuning. The efficiency and scalability of LightGBM made it a suitable choice for large datasets, although it displayed sensitivity to class imbalance. Catboost excelled in handling categorical features, but longer training times were observed for larger datasets. NB showcased simplicity and computational efficiency but assumed independence among features. KNN, known for its capability to capture local patterns and spatial relationships, was found to be sensitive to the choice of distance metric. GBM, while capturing complex relationships effectively, was prone to overfitting without proper regularization. DT, with its interpretability and ease of understanding, faced limitations in terms of overfitting and limited generalization. After dimensionality reduction, certain algorithms exhibited improvements in their AUC/ROC scores and average accuracy, including RF, EXT, XGboost, and LightGBM. However, for a few algorithms, such as NB and DT, a decrease in performance was observed. This study provides valuable insights into the performance characteristics, strengths, and limitations of various machine learning algorithms in classification tasks. Researchers and practitioners can utilize these findings to make informed decisions when selecting algorithms for their specific datasets and requirements. We also aim to identify the potential factors contributing to the high accuracy rates obtained from these ensembled algorithms and explore possible shortcomings of non-ensembled algorithms that may result in lower accuracy rates. By conducting a comprehensive analysis of these algorithms, we seek to provide valuable insights into the benefits and limitations of ensembled approaches for landslide susceptibility mapping. Our study sheds light on the challenges faced when balancing accuracy and complexity in machine learning models for landslide susceptibility mapping. It emphasizes the importance of carefully considering the level of complexity and entropy reduction in relation to the specific patterns and uncertainties present in the data. By providing insights into this tradeoff, our research aims to assist researchers and practitioners in making informed decisions regarding model complexity and entropy reduction, ultimately improving the quality and interpretability of landslide susceptibility maps.

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.

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.

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.

Deep neural networks (DNNs), founded on the brain's neuronal organization, can extract higher-level features from raw input. However, complex intellect via autonomous decision-making is way beyond current AI design. Here we propose an autonomous AI inspired by the thermodynamic cycle of sensory perception, operating between two information density reservoirs. Stimulus unbalances the high entropy resting state and triggers a thermodynamic cycle. By recovering the initial conditions, self-regulation generates a response while accumulating an orthogonal, holographic potential. The resulting high-density manifold is a stable memory and experience field, which increases future freedom of action via intelligent decision-making.

From physics to the social sciences, information is now seen as a fundamental component of reality. However, a form of information seems still underestimated, perhaps precisely because it is so pervasive that we take it for granted: the information encoded in the very environment we live in. We still do not fully understand how information takes the form of cities, and how our minds deal with it in order to learn about the world, make daily decisions, and take part in the complex system of interactions we create as we live together. This paper addresses three related problems that need to be solved if we are to understand the role of environmental information: (1) the physical problem: how can we preserve information in the built environment? (2) The semantic problem: how do we make environmental information meaningful? And (3) the pragmatic problem: how do we enact environmental information in our daily lives? Attempting to devise a solution to these problems, we introduce a three-layered model of information in cities, namely environmental information in physical space, environmental information in semantic space, and the information enacted by interacting agents. We propose forms of calculating entropy in these different layers, and apply these measures to archetypal urban cases and simulated scenarios. Our results suggest that ordered spatial structures and diverse land use patterns encode information, and that aspects of physical and semantic information affect coordination in interaction systems.

A convenient practical model for accurately estimating the total entropy (ΣSi) of atmospheric gases based on physical action is proposed. This realistic approach is fully consistent with statistical mechanics, but reinterprets its partition functions as measures of translational, rotational and vibrational action or quantum states, to estimate the entropy. With all kinds of molecular action expressed as logarithmic functions, the total heat required for warming a chemical system from 0o K (ΣSiT) to a given temperature and pressure can be computed, yielding results identical with published experimental third law values of entropy. All thermodynamic properties of gases including entropy, enthalpy, Gibbs energy and Helmholtz energy are directly estimated using simple algorithms based on simple molecular and physical properties, without resource to tables of standard values; both free energies are measures of quantum field states and of minimal statistical degeneracy, decreasing with temperature and declining density. We propose that this more realistic approach has heuristic value for thermodynamic computation of atmospheric profiles, based on steady state heat flows equilibrating with gravity. Potentially, this application of an action principle can provide better understanding of emergent properties of many natural or evolving complex systems, including modelling of predictions for global warming.

The article analyzes Bernoulli 's binary sequences in representation of empirical events about the distribution of natural resources and population sizes. Considering the event as a nonlinear system, and consisting of two dependent random variables, with memory and probabilities in maximum finite or infinite lengths, constant and equal to ½ for both variables (stationary process). The expressions of the possible trajectories remain constant in sequences that are repeated alternating the presence or absence of one of the variables at each iteration (asymmetric). There are constant oscillations in the event except if the variables X₁ and X₂ are regulated as a function of time Y. It is observed that the variables X₁ and X₂ assume in time T_k → ∞ specific behaviors (geometric variable) that can be used as management tools for random systems. In this way, the article seeks to know from this analyzes, the maximum entropy of information in the system by a theoretical view and how to model resources distribution or containment in the given problem.

The residual multiparticle entropy (RMPE) of a fluid is defined as the difference, Δs, between the excess entropy per particle (relative to an ideal gas with the same temperature and density), s_ex, and the pair-correlation contribution, s₂. Thus, the RMPE represents the net contribution to s_ex due to spatial correlations involving three, four, or more particles. A heuristic “ordering” criterion identifies the vanishing of the RMPE as an underlying signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is a typical example). Regardless of this, the knowledge of the RMPE is important to assess the impact of non-pair multiparticle correlations on the entropy of the fluid. Recently, an accurate and simple proposal for the thermodynamic and structural properties of a hard-sphere fluid in fractional dimension 1 < d < 3 has been proposed [Santos, A.; López de Haro, M. Phys. Rev. E 2016, 93, 062126]. The aim of this work is to use this approach to evaluate the RMPE as a function of both d and the packing fraction ϕ. It is observed that, for any given dimensionality d, the RMPE takes negative values for small densities, reaches a negative minimum Δs_min at a packing fraction ϕ_min, and then rapidly increases, becoming positive beyond a certain packing fraction ϕ₀. Interestingly, while both ϕ_min and ϕ₀ monotonically decrease as dimensionality increases, the value of Δs_min exhibits a nonmonotonic behavior, reaching an absolute minimum at a fractional dimensionality d ≃ 2.38. A plot of the scaled RMPE Δs/|Δs_min| shows a quasiuniversal behavior in the region −0.14 ≲ ϕ − ϕ₀ ≲ 0.02.

Bijective Analysis of 4D Minkowski space-time model confirms that 4D space-time where time would be 4th dimension of space does not exist. In 4D manifold, time is the duration of a physical event which runs in space. An event does not have the duration in time, duration itself is time. It means that any given physical phenomena can only be symmetric in space; not in time.

Voronoi entropy for the random patterns and patterns demonstrating various elements of symmetry are calculated. The symmetric patterns are characterized by the values of the Voronoi entropy very close to those inherent to random ones. This contradicts the idea that the Voronoi entropy quantifies the ordering of the seed points, constituting the pattern. The extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables revealing of the elements of symmetry of the pattern.

The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalized entropies crucially depend on the number of allowed number degrees of freedom $N$. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume $W$ on $N$. We review the ensuing entropies, discuss the composability axiom, relate to the Gibbs' paradox discussion and explain why group entropies may be particularly relevant from an information theoretic perspective.

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

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.

The maximization of entropy S within a closed system is accepted as an inevitability (as the second law of thermodynamics) by statistical inference alone. The Maximum Entropy Production Principle (MEPP) states that not only S maximizes, but $\dot{S}$ as well: a system will dissipate as fast as possible. There is still no consensus on the general validity of this MEPP, even though it shows remarkable explanatory power (both qualitatively and quantitatively), and has been empirically demonstrated for many domains. In this theoretical paper I provide a generalization of entropy gradients, to show that the MEPP actually follows from the same statistical inference, as that of the 2nd law of thermodynamics. For this generalization I only use the concepts of super-statespaces and microstate-density. These concepts also allow for the abstraction of 'Self Organizing Criticality' to a bifurcating local difference in this density, and allow for a generalization of the fundamentally unresolved concepts of 'chaos' and 'order'.

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.

Bello's stochastic linear time-varying system theory has been widely used in the wireless communications literature to characterize multipath fading channel statistics. In the context of radar backscatter, this formulation allows for statistical characterization of distributed radar targets in range and Doppler using wide-sense stationary uncorrelated scattering (WSSUS) models. WSSUS models separate the channel from the effect of the waveform and receive filter, making it an ideal formulation for waveform design problems. Of particular interest in the radar waveform design community is the ability to suppress unwanted backscatter from the earth's surface, known as clutter. Various methods for estimating WSSUS system functions have been studied in the literature, but to date, no analytic expressions for radar surface clutter range-Doppler scattering functions exist. In this work we derive a wideband generalization of the Jakes Doppler spectrum model, which is widely used in the wireless communications literature, adapt it for use in radar problems, and show how the maximum entropy method can be used to extend this model to account for internal clutter motion. Validation of the spectral and stationarity properties of the proposed model against a subset of the Australian Ingara sea clutter database is performed, and good agreement is shown.

Hyperspectral images are an important tool to assess ecosystem biodiversity both on terrestrial and benthic habitats. To obtain more precise analysis of biodiversity indicators that agree with indicators obtained using field data, analysis of spectral diversity calculated from images have to be validated with field based diversity estimates. The plant species richness is one of the most important indicators of biodiversity. This indicator can be measured in hyperspectral images considering the Spectral Variation Hypothesis (SVH) which states that the spectral heterogeneity is related to spatial heterogeneity and thus to species richness. The goal of this research is to capture spectral heterogeneity from hyperspectral images for a terrestrial neo tropical forest site using Vector Quantization (VQ) method and then use the result for prediction of plant species richness. The results are compared with that of Hierarchical Agglomerative Clustering (HAC). The validation of the process index is done calculating the Pearson correlation coefficient between the Shannon entropy from actual field data and the Shannon entropy computed in the images. Terrestrial dry forest and marine coastal hyperspectral images with different resolutions have been used for spectral diversity feature validation.

Study background and aims: Laparoscopic cholecystectomy is one of the most frequently performed interventions in departments of general surgery. One of the most important aims in achieving perioperative stability of these patients is diminishing the impact of general anesthesia on the hemodynamic stability and the optimization of anesthetic drug doses based on the individual clinical profile of each patient. The objective of this study is the evaluation of the impact monitoring the depth of anesthesia through Entropy (state entropy – SE and response entropy -RE) has on the hemodynamic stability and on the doses of volatile anesthetic. Material and Methods: This is a prospective, observational, randomized, monocentric study carried out between January 2019 and December 2019 in the Clinic of Anesthesia and Intensive Care from the “Pius Brînzeu” Emergency County Hospital in Timișoara, Romania. The patients included in the study were divided in two study groups; patients in Group A (target group) received multimodal monitoring that included monitoring of standard parameters and of Entropy (SE and RE), while patients in Group B (control group) only received standard monitoring. Anesthetic dose in group A were optimized to achieve a target entropy of 40-60. Results: 68 patients met the inclusion criteria and were allocated to one of the two study groups, Group A (N=43) and Group B (N=25). There were no statistically significant differences identified between the two groups for both demographical and clinical data (p>0.05). Statistically significant differences have been identified for the number of hypotensive episodes (p = 0.011, 95% CI 0.1851 to 0.7042) and for the number of episodes of bradycardia (p < 0.0001, 95% CI 0.3296 to 0.7923). Moreover, there was a significant difference in the Sevoflurane consumption between the two study groups (p = 0.0498, 95% CI -0.3942 to 0.9047). Conclusions: The implementation of the multimodal monitoring protocol that includes the standard parameters and the measurement of Entropy for determining the depth of anesthesia (SE and RE) lead to a considerable improvement in perioperative hemodynamic stability. Optimizing the doses of anesthetic drugs based on the individual clinical profile of each patient leads to a considerable decrease in drug consumption as well as to a lower incidence of hemodynamic side-effects.

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.

Autofocus is an essential part of the SAR imaging process. Multi-subaperture autofocus algorithm is a commonly used autofocus algorithm for processing SAR stripmap mode data. The multi-subaperture autofocus algorithm has two main steps, the first is to estimate the phase error gradient within the subaperture, the second is to splice the phase error gradient, that is, to remove the shift amount between the estimated adjacent subapertures’ error gradients. Previous gradient-splicing algorithms assume that the estimation of subaperture error is accurate, but when the estimation of subaperture phase error gradients is not accurate enough, these algorithm performance will be degraded. A new phase error gradient splicing algorithm is proposed in this paper. It roughly estimates the shift amount first, and then finely estimates the shift amount based on the minimum-entropy criterion, which can improve the robustness of splicing especially when the estimation of the phase error gradients of the subaperture is not accurate enough. To speed up the algorithm, a variable-step-size search method is used. Simulation and experimental results show that the algorithm has enough accuracy and still has good performance when other splicing algorithms doesn’t perform well.

The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still correspond to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea current at the time that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be done in a reversible process rather than the work that was actually done. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step-change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appro-priately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work done in-ternally and externally.

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.

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.

This is a review of efforts to discover action principles for Hydrodynamics and Thermodynamics. The work began with a determined attempt to create sources for Einstein's equations that describe continuous matter - as opposed to point particles. This requires a relativistic action principle. This report is mainly about (non relativistic) Adiabatic Thermodynamics, non equilibrium thermodynamics based on the method of Gibbs. The main relations of classical thermodynamics can be derived from an action principle, in the classical global form and in the local form advocated by Callen. The entropy is defined as the negative derivative of the free energy (free energy density) with respect to the volume (density). This is integrated with an action principle for hydrodynamics that was known to Lagrange in 1760. It is strongly limited to irrotational velocity fields, nevertheless it provides the needed Lagrangian for a large part of thermodynamics. This is the subject of the first 3 sections. It includes a brief review of a new theory of mixtures. The most difficult part of the program has been the discovery of Conservative Hydrodynamics with the required four independent degrees of freedom, with general flows. We give an account of the genesis and the structure of this theory, then a tour of recent applications.

The Landauer principle supplies the estimation of the minimal mass of a particle which is capable to record/erase information within a thermal bath at the temperature of T. Particles lighter than ${\tilde{m}}_0=\frac{k_{B}Tln2}{c^2}$will not transform the information to the surrounding bodies and are well expected to be undetectable. The relation of the Landauer principle to the problem of “dark matter” is discussed. The maximal informational content of a particle at rest, estimated as $I_{max}=\frac{m_0{c}^2}{k_{B}Tkn2}$ is introduced. The Landauer principle also allows the estimation of minimal energy of the field which is capable to record/erase 1 bit of information in the surrounding at the temperature of T. The relativistic aspects of the Landauer principle and its relation to the relativistic transformation of temperature are addressed.

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.

This paper presents the automation of the thin-layer chromatography technique whose separation and identification of molecules present in a mixture are currently done manually and laboriously [1]. We have therefore found an interest in automating this technique. In this part, the method implemented comprises 2 steps. First we proceeded to the segmentation of the spots obtained on the chromatographic plate. We then developed a program to identify families of molecules such as coumarins, terpenes, tannins, flavonoids, polyphenols, etc. by calculating segmentation parameters such as standard deviation, entropy, average pixel intensity from an algorithm on the matlab software. Finally our results have been compared to the results obtained by the traditional identification technique in laboratories. Some similarity between the two results obtained shows the reliability and the robustness of our technique.

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 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.

Solidification cracking is a major obstacle when joining dissimilar alloys using additive manufacturing. In this work, location-specific solidification cracking susceptibility has been investigated using an integrated computational materials engineering (ICME) approach for a graded alloy formed by mixing P91 steel and Inconel 740H superalloy. An alloy derived from a mixture of 26 wt.% P91 steel and 74 wt.% Inconel 740H, with high configurational and total entropy, was fabricated using wire-arc additive manufacturing. Microstructure characterization revealed intergranular solidification cracks, which increased in length along with the build height. With inputs from experiments, such as secondary dendrite arm spacing, the DICTRA (diffusion-controlled transformations) module within the Thermo-Calc software was used to model location-specific solidification cracking susceptibility. The top region, with the highest cooling rate, has the highest solidification cracking susceptibility and is in good agreement with the experimentally observed crack length. From Scheil simulations, it was deduced that pronounced segregation of Nb and Cu within the cracks increased the solidification range by suppressing the solidus temperature. The overall solidification cracking susceptibility and freezing range was highest for the 26 wt.% P91 alloy amongst the mixed compositions between P91 steel and 740H superalloy, proving that solidification characteristics play a major role in alloy design for additive manufacturing.

The time’s arrow of macroscopic physical phenomenon is reflected by irreversible physical process, which essentially occurs from small probability state to high probability state. In this paper, simplified models are proposed to understand the macroscopic physical process. In order to describe the information of a physical system, we defined the full self-information as "information height" to describe the complexity or difficulty of a macrostate of physical system. In this way, the direction of macroscopic physical process is from high information height to low information height. We can judge the direction of physical process by the information height. If we want the macroscopic physical process to evolve from the low information height state to the high information height state, the system need to add extra information and corresponding energy to increase the information height.

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.

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches on it, we show that entropy has a universal stochastic definition which is not disorder. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept and promotes entropy as the mother of creativity and evolution. As social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether the maximum entropy, applied to the distribution of wealth quantified by annual income, can give an objective description. Using publicly available income data, we show that the income distribution is consistent with the principle of the maximum entropy. The increase of entropy is associated to increase of society’s wealth yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in development and increase of the entropy of income. Such findings are contrary to the theories of ecological economics and other theories which use the term entropy in a Malthusian perspective.

The Schelling model of segregation allows for a general description of residential movements in an environment modeled by a lattice. The key factor is that occupants change positions until they are surrounded by a designated minimum number of similarly labeled residents. An analogy to the Ising model has been made in previous research, primarily due the assumption of state changes being dependent upon the adjacent cell positions. This allows for concepts produced in statistical mechanics to be applied to the Schelling model. Here is presented a methodology to estimate the entropy of the model for different states of the simulation. A Monte Carlo estimate is obtained for the set of macrostates defined as the different aggregate homogeneity satisfaction values across all residents, which allows for the entropy value to be produced for each state. This produces a trace of the estimated entropy value for the states of the lattice configurations to be displayed with each iteration. The results show that the initial random placements of residents have larger entropy values than the final states of the simulation when the overall homogeneity of the residential locality is increased.

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.

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.

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.

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.

How to build an optimal model where three terms “time, causality, and entropy” will be interrelated in a most correct way? This task has a semantic and physical aspect. We give in this article the solution that is based only on elementary perception. In physics, we experience time with our senses as the duration of material change running in space. This fact is the standpoint for our model where causality is only a principle, it is not a physical actuality and entropy runs only in space and not in time. Time is merely a duration of entropy increasing and is entering existence when measured by the observer.

In this letter, instead of choosing the Einstein Rosen bridge between two black holes as in ER=EPR, we consider a wormhole between a black hole and a closed edge of the wormhole. We assume that information in a black hole travels through a wormhole, turns to mass (dark matter) in the closed region. This study is in contradiction with the existence of the white hole in our Universe. We replace the notion of the white hole with the massive closed region. We prove the metric of the closed region by the Hopf fibration, this new metric generalizes the $AdS_{5}$\ metric.

The emergence of various electronic devices and equipment such as electric vehicles and drones requires higher energy density energy storage devices. Lithium-sulfur batteries (LSBs) are considered as the most promising new generation energy storage system owing to high theoretical specific capacity and energy density. However, the severe shuttle behaviors of soluble lithium polysulfides (LiPSs) and the slow redox kinetics lead to low sulfur utilization and poor cycling stability, which seriously hinder the commercial application of LSBs. Therefore, various catalytic materials have been employed to solve these troublesome problems. High entropy materials (HEMs), as advanced materials, can provide unique surface and electronic structures that expose plentiful catalytic active sites, which opens new ideas for the regulation of LiPSs redox kinetics. Notwithstanding many instructive reviews in the land of LSBs, while this review aims to offer a complete and shrewd summary of the current progresses in HEMs-based LSBs, including in-depth interpretation of design principles and mechanistic electrocatalysis functions as well as pragmatic perspectives.

Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the3literature of non-equilibrium statistical mechanics. This article provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the5mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics

The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of scienThe Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.ce, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.

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.

Physics has been thought to truly represent reality since at least Galileo, and the foundations of physics are always established using philosophical ideas. In particular, the elegant naming of physical entities is usually very influential in the acceptance of physical theories. We here demonstrate (using current developments in thermodynamics as an example) that both the epistemology and the ontology of physics ultimately rest on poetic language. What we understand depends essentially on the language we use. We wish to establish our knowledge securely, but strictly speaking this is impossible using only analytic language. Knowledge of the meanings of things must use a natural language designed to express meaning, that is, poetic language. Although the world is really there, and although we can indeed know it truly, this knowledge is never either complete or certain but ultimately must rest on intuition. Reading a recently discovered artefact with a palaeo-Hebrew inscription as from the first century, we demonstrate from it that this ontological understanding long predates the Hellenic period. Poetic language is primary, both logically and temporally.

We investigate the physics of a medium-size quantum particle' gases, of the order of hundreds or thousands of fermions/bosons (far below the thermodynamic limit $N \, \rightarrow \, 10^{24}$). Appeal to microcanonical ensemble becomes then unavoidable. The so-called statistical complexity is our protagonist. Interesting facts are uncovered, both for fermions and bosons, yielded by statistical quantifiers.

We derive time evolution equations, namely the Schrodinger-like equations and the Klein-Gordon equations for coherent fields and the Kadanoff-Baym (KB) equations for quantum fluctuations, in Quantum Electrodynamics (QED) with electric dipoles in 2 + 1 dimensions. Next we introduce a kinetic entropy current based on the KB equations in the 1st order of the gradient expansion. We show the H-theorem for the Leading-Order self-energy in the coupling expansion (the Hartree-Fock approximation). We show a conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to Quantum Brain Dynamics, that is QED with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain.

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

In computational neuroscience, spiking neurons are often analyzed as computing devices that register bits of information, with each action potential carrying at most one bit of Shannon entropy. Here, I question this interpretation by using Landauer's principle to estimate an upper limit for the quantity of thermodynamic information that can be dissipated by a single action potential in a typical mammalian neuron. I show that an action potential in a typical mammalian cortical pyramidal cell can carry up to approximately 3.4e11 natural units of thermodynamic information, or about 4.9e11 bits of Shannon entropy. This result suggests that an action potential can process much more information than a single bit of Shannon entropy.

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that excludes the existence of non-Shannon inequalities. It is demonstrated that planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.

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.

It is well known that the Continuous Galerkin Finite Element (CGFE) method is globally consistent with respect to the first law of thermodynamics. This means that, for any mesh, all obtained discrete solutions will conserve total energy. One might expect, that the method is, also, globally consistent with respect to the second law of thermodynamics. In this paper, we formally study if such conjecture is true. The heat conduction equation is used as the physical model for this analysis. In the present study it is proved that the conjecture is false: at least, for standard piecewise linear (1D and 2D) elements, the CGFE method is not always globally consistent with respect to the second law of thermodynamics. In other words, some obtained discrete solutions can violate the global postulate of the second law, which asserts that total entropy can never decrease.

The Brahmaputra is one of the largest rivers in the world, ranking fifth in average discharge. As a result, it is heavily braided with various intricate paths in order to dissipate its huge energy. Although this river is normally classed as a braided river, it has recently been classified as an anastomosing river due to its multi-channel features over alluvial plains. Additionally, the Brahmaputra river’s morphology is random in nature as a result of its high flow variability and bank erodibility. Its anastomosing planform changes in response to seasonal water and sediment waves, resulting in a morphology that is extremely complex. The purpose of this study is to examine the Brahmaputra river’s anastomosing planform entropy as a measure of complexity, power spectral density as a measure of fluctuation and their relationship to the energy expenditure as an imprint of flflow rate of river systems on alluvial landscapes.

The information entropy for Smoluchowski coagulation equation is proposed based on statistical mechanics. And the normalized particle size distribution is a lognormal function at equilibrium from the principle of maximum entropy and moment constraint. The geometric mean volume and standard deviation in the distribution function are determined as simple constant. The results reveal that the assumption that algebraic mean volume be unit in self-preserving hypothesis is reasonable in some sense. Based on the present definition of information entropy, the Cercignani’s conjecture holds naturally for Smoluchowski coagulation equation. Together with the proof that the conjecture is also true for Boltzmann equation, Cercignani’s conjecture will holds for any two-body collision systems, which will benefit the understanding of Brownian motion and molecule kinematic theory, such as the stability of the dissipative system, and the mathematical theory of convergence to thermodynamic equilibrium.

The prevailing interpretations of physics are based on deeply entrenched assumptions, rooted in classical mechanics. Logical implications include: the denial of entropy as a fundamental physical property, and the inability to explain irreversible change, random quantum measurements, or nonlocality without untestable and implausible metaphysical implications. We propose a conceptual model that is based on empirically justifiable assumptions and consistent with observations. The WYSIWYG Conceptual Model (WCM) assumes no hidden properties: “What You can See Is What You Get.” The WCM contextually defines a system’s state with respect to its actual ambient background, and it extends existing models of physical reality by defining entropy and exergy as objective contextual properties of state. The WCM establishes the irreversible dissipation of exergy and the Second law of thermodynamics as a fundamental law of physics, it recognizes physical randomness, and it provides a physical explanation for nonlocality, consistent with Special Relativity, without hidden variables, superdeterminism, or “spooky action.”

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of the generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss generating function approach using which we derive different entropy measures. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.

Double-spiral galaxies are common in the Universe. It is known that the logarithmic double spiral is a Maximum Entropy geometry and represents spiral galaxies well. It is also known that the virial mass of such a galaxy can be approximately determined from the entropy of its central supermassive black hole. But over time the black hole must accrete mass, and therefore the overall galactic entropy must increase. From the associated entropic Euler-Lagrange equation (forming the basis of the Principle of Least Exertion, and also enabling the application of Nöther’s theorem) we show that the galactic entropy production is a conserved quantity, and we derive an appropriate expression for the relativistic entropic Hamiltonian of an idealised spiral galaxy. We generalise Onsager’s celebrated expression for entropy production and demonstrate that galactic entropy production has two parts, one many orders of magnitude larger than the other, and where the smaller is comparable to the Hawking radiation of the central supermassive black hole. We conclude that galaxies cannot be isolated, since even idealised spiral galaxies have non-zero entropy production.

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.

We reduplicate the Book “Dark Energy” by M. Li, X-D. Li, and Y. Wang, given zero-point energy calculation with an unexpected “length’ added to the ‘width’ of a graviton wave just prior to specifying the creation of ‘gravitons’, using the Rosen and Israelit model of a nonsingular universe. In doing so we are in addition to obtaining a wavelength 10^30 times greater than Planck’s length so we can calculate DE, may be able to with the help of the Rosen and Israelit model have a first approximation as to the arrow of time, and a universe with massive gravity. We have left the particulars of the nonsingular starting point undefined but state that the Rosen and Israelit model postulates initial temperatures of 10^-180 Kelvin and also a value of about Planck temperature, at 10^-3 centimeters radii value which may satisfy initial conditions asked by t’Hooft for describing an arrow of time. A key assumption is that the DE is formed at 10^-3 cm, after an expansion of 10^30 times in radii, from the Planck length radius nonsingular starting point. The given starting point for DE in this set of assumptions is where there is a change in the cosmic acceleration, to a zero value, according to Rosen and Israel, with time t = 1.31 times 10^-42 seconds. Which may be where we may specify a potential magnitude, V, which has ties into inflaton physics. The particulars of the model from Rosen and Israelit allow a solution to be found, without discussion of where that nonsingular starting point came from, a point the author found in need of drastic remedies and fixes.

The chicken embryo is a widely used experimental animal-model in many studies such as developmental biology and to study the physiological responses and adaptation to altered environments as well as for cancer and neurobiology research. Embryonic heart rate is an important physiological variable useful as an index reflecting the embryo's natural activity and is considered one of the most difficult parameters to measure. An acceptable measurement technique of embryonic heart rate should provide a reliable cardiac signal quality while maintaining adequate gas exchange through the eggshell along the incubation and embryonic developmental period. In this paper, we presented a detailed design and methodology for a non-invasive PPG-based prototype (Egg-PPG) for real-time and continuous monitoring of embryonic heart rate during incubation. An automatic embryonic cardiac wave detection algorithm, based on normalised spectral entropy, is described. The developed algorithm successfully estimated the embryonic heart rate with 98.7% accuracy. We believe that the developed overall system presented in this paper is showing a promising solution for non-invasion, real-time monitoring of embryonic cardiac signal, which can be used in both experimental studies (e.g., developmental embryology and cardiovascular research) and in industrial incubation applications.

We introduce an information theoretic framework for a quantitative measure of originality to model the impact of various classes of biases, errors and error corrections on scientific research. Some of the open problems are also outlined.

The study of order patterns of three equally spaced values $x_t,x_{t+d},x_{t+2d}$ in a time series is a powerful tool. The lag $d$ is changed in a wide range so that differences of frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, outliers and missing data do not matter. On the theoretical side, we study properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions.

Classification of electromyographic signals has a wide range of applications, from clinical diagnosis of different muscular diseases to biomedical engineering, where their use as input control of prosthetic devices has become a hot topic of research. Challenge of classifying this signals relies on the accuracy of the proposed algorithm and the possibility of its implementation on hardware. This paper consider the problem of electromyography signal classification, solved with the proposed signal processing and feature extraction stages, with focus lying on the signal model and time domain characteristics for better classification accuracy. The proposal considers a simple preprocessing technique that produces signals suitable for feature extraction, and the Burg reflection coefficients to form learning and classification patterns. These coefficients yield a competitive classification rate compared to used time domain features. Sometimes, the feature extraction from electromyographic signals showed that procedure can omit less useful traits for machine learning models. Using feature selection algorithms provides a higher classification performance with as fewer traits as possible. Algorithms achieved a high classification rate up to 100% with low pattern dimensionality, with other kinds of uncorrelated attributes for hand movement identification.

Several optimization models of irreversible reverse cycle machines have been developed based on different optimization criteria in the literature, most of them using linear heat transfer laws at the source and sink. This raises the issue how close to actual operation conditions they are, since the heat transfer law on the phase-change processes is dependent on ΔT3. This paper addresses this issue by proposing a general model for study and optimization of thermal machines with two heat reservoirs applied to a Carnot-like refrigerator, with non-linear heat transfer laws and internal and external irreversibility. The optimization was performed using First and Second Law of Thermodynamics and Lagrange multipliers method. Thus, several constraints were imposed to the system, also different objective functions were considered, allowing finding the optimum operating conditions, as well as the limited variation ranges of the system parameters. Results show that the nature of the heat transfer laws affects the optimum values of system parameters for obtaining maximum performances and also their magnitude. Sensitivity studies with respect to system several parameters are presented. The results contribute to the understanding of the system limits in operation under different constraints and allow choosing the most convenient variables in given circumstances.

Graph entropies have been used to interpret the complexity of the networks. There are various graph entropies in the literature. In this note a new graph entropy is defined which is based on the dominating sets of the graphs. Moreover the entropy of some classes of the graphs is obtained

In this paper, the definition of information entropy of Smoluchowski coagulation equation for Brownian motion is introduced based on coagulation probability. The expression of entropy is the function of geometric average particle volume and standard deviation with lognormal distribution assumption. The asymptotic solution with moment method shows that the entropy is a monotone increasing function of time, which is equivalence to the entropy based on particle size distribution. the result reveals that the present definition of entropy of Smoluchowski coagulation equation are inadequate because the particle average volume at equilibrium cannot be determined from the principle of maximum entropy. This provides a basis for further exploring the global properties of Smoluchowski coagulation equation.

We write the mutual information between an input speech utterance and its reconstruction by a Code-Excited Linear Prediction (CELP) codec in terms of the mutual information between the input speech and the contributions due to the short term predictor, the adaptive codebook, and the fixed codebook. We then show that a recently introduced quantity, the log ratio of entropy powers, can be used to estimate these mutual informations in terms of bits/sample. A key result is that for many common distributions and for Gaussian autoregressive processes, the entropy powers in the ratio can be replaced by the corresponding minimum mean squared errors. We provide examples of estimating CELP codec performance using the new results and compare to the performance of the AMR codec and other CELP codecs. Similar to rate distortion theory, this method only needs the input source model and the appropriate distortion measure.

Attempts to find and quantify the supposed low entropy of organisms and its preservation are revised. Absolute entropy of the mixed components of non-living biomass (around -1.6 x 103 J K-1 L-1) is the reference to which other entropy decreases would be ascribed to life. Compartmentation of metabolites and departure from the equilibrium of metabolic reactions account for 1 and 40-50 J K-1 L-1, respectively, decreases of entropy and, though small, are distinctive features of living tissues. DNA and proteins do not supply significant decreases of thermodynamic entropy, but their low informational entropy is relevant for life and its evolution. No other living feature contributes significantly to the low entropy associated to life. The photosynthetic conversion of radiant energy to biomass energy accounts for the most of entropy (2.8 x 105 J K-1 carbon kg-1) produced by living beings. The comparative very low entropy produced in other processes (around 4.8 x102 J K-1 L-1 day-1 in human body) must be rapidly exported outside as heat to preserve the low entropy decreases due to compartmentation and non-equilibrium metabolism. Enzymes and genes are described whose control minimize the rate of production of entropy and could explain selective pressures in biological evolution and the rapid proliferation of cancer cells.

According to Landauer’s principle, the energy of a particle may be used to record or erase N number of information bits within the thermal bath. The maximum number of information N recorded by the particle in the heat bath is found to be inversely proportional to its temperature T. If at least one bit of information is transferred from the particle to the medium, then the particle might exchange information with the medium. Therefore for at least one bit of information, the limiting mass that can carry or transform information assuming a temperature T= 2.73 K is equal to m = 4.71810-40 kg which is many orders of magnitude smaller that the masse of most of today’s elementary particles. Next, using the corresponding temperature of a graviton relic and assuming at least one bit of information the corresponding graviton mass is calculated and from that, a relation for the number of information N carried by a graviton as a function of the graviton mass mgr is derived. Furthermore, the range of information number contained in a graviton is also calculated for the given range of graviton mass as given by Nieto and Goldhaber, from which we find that the range of the graviton is inversely proportional to the information number N. Finally, treating the gravitons as harmonic oscillators in an enclosure of size R we derive the range of a graviton as a function of the cosmological parameters in the present era

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defined taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The efficacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

In the upper charged layers of the atmosphere, the plasma is very rarefied. The collisions between its molecules are almost non-existent, and the driving forces behind them are the Lorentz forces resulting from the electric and magnetic fields. For this reason, we are interested in studying the behavior of non-collision plasmas because of its essential applications, such as the movement of satellites in the charged atmosphere. In this paper, the flow problem of collisionless gaseous plasma is examined. For that propose, we solve the unsteady Vlasov-Maxwell system of non-linear partial differential equations analytically. Methods of moments and traveling wave parameters are used to acquire an exact solution. Specific macroscopic properties of collisionless gaseous plasma are calculated along with electrical and magnetic fields. Further, thermodynamic estimation, such as entropy and entropy production, is presented. Those calculations allow us to measure the consistency with the laws of non-equilibrium thermodynamics. Relations between internal energy modification participations are predicted using Gibbs' equation for collisionless plasma. The modification effect of internal energies due to electro-magnetic fields is found to be small compared with the internal energy change due to the effect of entropy. That is because these fields are self-induced by plasma particles due to the sudden movement of the rigid plane plate. The results are accomplished according to the typical argon gaseous plasma model. Three-dimensional diagrams showing the measured variables are drawn to investigate and discuss their behavior. The problem has many commercial applications for the movement of objects in the charged atmosphere.

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 practice of spatial econometrics revolves around a weighting matrix, which is often supplied by the user on previous knowledge. This is the so called $\mathbf{W}$ issue. Probably, the aprioristic approach is not the best solution although, nowadays, there few alternatives for the user. Our contribution focuses on the problem of selecting a $\mathbf{W}$ matrix from among a finite set of matrices, all of them considerer appropriate for the case. We develop a new and simple method based on the Entropy corresponding to the distribution of probability estimated for the data. Other alternatives, which are common in current applied work, are also reviewed. The paper includes a large Monte Carlo to calibrate the effectiveness of our approach compared to the others. A well-known case study is also included.

Recent works in mechanical fatigue consider that a threshold of entropy exists, the fracture fatigue entropy. The determination of this quantity is usually done considering empirical models for the mechanical power estimation. In this paper, we experimentally observe the existence of a threshold of entropy and exergy in low cycle fatigue for a flat Al-2024 specimen avoiding the use of a model, solely measuring the heat generated during a fatigue test. Results are then compared considering various hypotheses (1D heat dissipation with convection and radiation considered as heat sources, and, heat transfer from a fin with convection and radiation as boundary conditions) to an empirical mechanical model known in the literature and deviations between them are discussed.

The black hole information paradox is one of the most puzzling paradoxes in physics. Black holes trap everything that falls into them, while their mass may leak away through purely thermal Hawking radiation. When a black hole vanishes, all the information locked inside, if any, is just lost, thus challenging the principles of quantum mechanics. However, some information does have a way to escape from inside the black hole, that is, through gravitational waves. Here, a concise extension of this notion is introduced. When a black hole swallows something, whether it is a smaller black hole or an atom, the system emits gravitational waves carrying the information about the “food”. Although most of the signals are too weak to be detected, the information encoded within them will persist in the universe. This speculation provides an explanation for a large part, if not all, of the supposed “information loss” in black holes, and thus reconciles the predictions of general relativity and quantum mechanics.

(1) Background: In nervous system information is conveyed by a sequence of action potentials, called spikes-trains. As MacKay and McCulloch proposed, spike-trains can be represented as bits sequences coming from Information Sources. Previously, we studied relations between Information Transmission Rates (ITR) carried out by the spikes, their correlations, and frequencies. Here, we concentrate on the problem of how spikes fluctuations affect ITR. (2) Methods: The Information Theory Method developed by Shannon is applied. Information Sources are modeled as stationary stochastic processes. We assume such sources as two states Markov processes. As a spike-trains' fluctuation measure, we consider the Standard Deviation sigma, which, in fact, measures average fluctuation of spikes around the average spike frequency. (3) Results: We found that character of ITR and signal fluctuations relation strongly depends on the parameter s which is a sum of transitions probabilities from no spike state to spike state and vice versa. It turned out that for smaller s (s<1) the quotient ITR\sigma has a maximum and can tend to zero depending on transition probabilities. While for s large enough (1<s) the ITR\sigma is separated from 0 for each s. Similar behavior was observed also when we replaced Shannon entropy terms in Markov entropy formula by their approximation with polynomials. We also show that the ITR quotient by Variance behaves in a completely different way. (4) Conclusions: Our results show that for large transition parameter s the Information Transmission Rate by sigma will never decrease to zero. Specifically, for 1<s<1.7 the ITR will be always, independently on transition probabilities which form this s, above the level of fluctuations, i.e. in this case we have sigma<ITR. Thus, we conclude that in a more noisy environment, to get appropriate reliability and efficiency of transmission, Information Sources with higher tendency of transition from the state no spike to spike state and vice versa should be applied.

In this paper, by extending some results of informational genomics, we present a new randomness test based on the empirical entropy of strings and some properties of repeatability and unrepeatability of substrings of certain lengths. We give the theoretical motivations of our method and some experimental results of its application to a wide class of strings: decimal representations of real numbers, roulette outcomes, logistic maps, linear congruential generators, quantum measurements, natural language texts, and genomes. It will be evident that the evaluation of randomness resulting from our tests does not distinguish among the different sources of randomness (natural, or pseudo-casual).

Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle still linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv=mr2ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@=mr2ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink, the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, that Carnot identified as reversible temperature-dependent but unequal exchanges in caloric. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’ exclusively to negative Gibbs energy (-G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates.

Clustering algorithms for multi-database mining (MDM) rely on computing $(n^2-n)/2$ pairwise similarities between $n$ multiple databases to generate and evaluate $m\in[1, (n^2-n)/2]$ candidate clusterings in order to select the ideal partitioning which optimizes a predefined goodness measure. However, when these pairwise similarities are distributed around the mean value, the clustering algorithm becomes indecisive when choosing what database pairs are considered eligible to be grouped together. Consequently, a trivial result is produced by putting all the $n$ databases in one cluster or by returning $n$ singleton clusters. To tackle the latter problem, we propose a learning algorithm to reduce the fuzziness in the similarity matrix by minimizing a weighted binary entropy loss function via gradient descent and back-propagation. As a result, the learned model will improve the certainty of the clustering algorithm by correctly identifying the optimal database clusters. Additionally, in contrast to gradient-based clustering algorithms which are sensitive to the choice of the learning rate and require more iterations to converge, we propose a learning-rate-free algorithm to assess the candidate clusterings generated on the fly in a fewer upper-bounded iterations. Through a series of experiments on multiple database samples, we show that our algorithm outperforms the existing clustering algorithms for MDM.

Information-related measures are useful tools for multi-variable data analysis, as measures of dependence among variables, and as descriptions of order and disorder in biological and physical systems. Measures, like marginal entropies, mutual / interaction / multi -information, have long been used in a number of fields including descriptions of systems complexity and biological data analysis. The mathematical relationships among these measures are therefore of significant inherent interest. Relations between common information measures include the duality relations based on Möbius inversion on lattices. These are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). While these relationships are of significant interest there has been, to our knowledge, no systematic examination of the full range of relationships of this diverse range of functions into a unifying formalism as we do here. In this paper we define operators on functions on these lattices based on the Möbius inversions that map functions into one another (Möbius operators). We show that these operators form a simple group isomorphic to the symmetric group S₃. Relations among the set of functions on the lattice are transparently expressed in terms of the operator algebra, and, applied to the information measures, can be used to derive a wide range of relationships among diverse information measures. The Möbius operator algebra is naturally generalized which yields extensive new relationships. This formalism now provides a fundamental unification of information-related measures, and the isomorphism of all distributive lattices with the subset lattice implies an even broader application of these results.

This study aimed to apply different complexity-based methods to surface electromyography (EMG) in order to detect neuromuscular changes after realistic warm-up and stretching procedures. Sixteen volunteers conducted two experimental sessions. They were tested before, after a standardized warm-up, and after a stretching exercise (static or neuromuscular nerve gliding technique). Tests included measurements of the knee flexion torque and EMG of biceps femoris (BF) and semitendinosus (ST) muscles. EMG was analyzed using the root mean square (RMS), sample entropy (SampEn), percentage of recurrence and determinism following a recurrence quantification analysis (%Rec and %Det) and a scaling parameter from a detrended fluctuation analysis. Torque was significantly greater after warm-up as compared to baseline and after stretching. RMS was not affected by the experimental procedure. In contrast, SampEn was significantly greater after warm-up and stretching as compared to baseline values. %Rec was not modified but %Det for BF muscle was significantly greater after stretching as compared to baseline. The a scaling parameter was significantly lower after warm-up as compared to baseline for ST muscle. From the present results, complexity-based methods applied to the EMG give additional information than linear-based methods. They appeared sensitive to detect EMG complexity increases following warm-up.

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.