The world is now undergoing through a global emergency due to COVID-19 which needs immediate remedies in order to strengthen the healthcare facility to save the nations. Looking towards to the remedies, research on different aspects including the genomic and proteomic level characterizations of the SARS-CoV2 are necessarily important. In this present study, the spatial representation/composition of twenty amino acids across the primary protein sequences of SARS-CoV2 have been looked into through different parameters viz. Shannon entropy, Hurst exponent in order to fetch the autocorrelation and amount of information over the spatial representations. Also frequency distribution of each of the amino acids over the protein sequences have been chalked out.

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

The notion of the informational measure of symmetry is introduced according to: HsymG=-i=1kPGilnPGi, where PGi is the probability of appearance of the symmetry operation Gi within the given 2D pattern. HsymG is interpreted as an averaged uncertainty in the presence of symmetry elements from the group G in the given pattern. The informational measure of symmetry of the “ideal” pattern built of identical equilateral triangles is established as HsymD3=1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, Hsym=0. Informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. Informational measure of symmetry does not correlate neither with the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns.

{Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighbouring values in a time series. This makes it possible to describe the signal as efficiently as prior proposed parameters such as permutation entropy (PE) or modified permutation entropy (mPE), but (1) reduces the size of the sample that is necessary to estimate the parameter value, and (2) enables the use of the Kullback-Leibler divergence to estimate the "distance" between the time series data and random signals.

Monitoring the ratio of forested and deforested areas plays a key role in studying the dynamics of forest areas. Appropriate mapping of anthropogenic forest disturbances is particularly important in the context of sustainable forest management. It provides ecological, social and economic information which is crucial for forest policymakers. In the last two decades, the forest areas of the Moldo-Transylvanian Carpathians have been subject to a high rate of deforestation which at present state lacks proper quantification. We present a novel methodology for monitoring the forest disturbance dynamics in Moldo-Transylvanian Carpathians by use of fractal analysis including entropy, Fractal Fragmentation Index (FFI) and Tug-of-War lacunarity (Λ_(T-o-W)). This was necessary to quantify and identify the disorder (entropy), the fragmentation (FFI) and heterogeneity of the spatial distribution (Λ_(T-o-W)) patterns. Based on satellite images of the forest areas (annually 2000-2014), increased fragmentation was demonstrated by FFI increase, a measure of the degree of disorder (entropy) and heterogeneity (lacunarity). Our results revealed that textural and fractal analysis can be an effective tool for the extraction of quantitative information about the spatiotemporal dynamics of forest disturbance. The methods developed, and results obtained are a complementary approach to forest disturbance mapping (based on traditional image classification) for future development and adaptation of forestry management policies to ensure a sustainable management and exploitation of forest areas.

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.

In this paper, we investigate the cumulative historical entropy of the lifetime of an n-component coherent system under the assumption that all system components have failed at time t. Using the system signature, we can calculate the cumulative historical entropy of the system’s lifespan, which is an important aspect in determining a system’s predictability. This research produces a number of significant results, including expressions, bounds, and ordering aspects for this measure. In addition, we offer a method for finding a preferred system based on cumulative Kullback-Leibler discriminating information that is closely related to the parallel system. These findings provide important insights into the predictability and dependability of coherent systems, emphasizing the importance of this field.

Diversity as well as temporal and spatial changes of the proportional abundances of different antibiotics (cycling, mixing or combinations thereof) have been hypothesised to be an effective administrative control strategy in hospitals to reduce the prevalence of antibiotic-resistant pathogens in nosocomial or community-acquired infections. However, a rigorous assessment of the efficacy of these control strategies is lacking. The main purpose here is to present a mathematical framework for the assessment of control stategies from a processual stance. To this end, we adopt diverse measures of heterogeneity and diversity of proportional abundances based on the concept of entropy from other fields and adapt them to the needs in assessing the impact of variations in antibiotic consumption on antibiotic resistance. Thereby, we derive a family of diversity measures whose members exhibit different degrees of complexity. Most important, we extent these measures such that they account for the assessment of temporal changes in heterogeneity including otherwise undetected diversity-invariant permutations of antibiotics consumption and prevalence of resistant pathogens. We apply a correlation analysis for the assessment of associations between changes of heterogeneities on the antibiotics and on the pathogen side. As a showcase, which serves as a proof-of-principle, we apply the derived methods to records of antibiotic consumption and prevalence of antibiotic-resistant germs from University Hospital Dresden. Besides the quantification of heterogeneities of antibiotics consumption and antibiotic resistance, we show that a reduction of prevalence of antibiotic-resistant germs correlates with a temporal change of similarity with respect to the first observation of antibiotics consumption, although heterogeneity remains approximately constant. Although an interventional study is pending, our mathematical framework turns out to be a viable concept for the assessment and optimisation of control strategies intended to reduce antibiotic resistance.

In 2020, the pandemic caused by the Coronaviruses (CoV) that are a large family of viruses that cause illness ranging from the common cold to more severe diseases such as Middle East Respiratory Syndrome (MERS-CoV) and Severe Acute Respiratory Syndrome (SARS-CoV2). The Coronavirus disease (COVID-19) is a new strain that was discovered in 2019 and has not been previously identified in humans. It is the high time to investigate the quantitative and/or qualitative genomic informations of the virus SARS-CoV2 in order to strengthen the healthcare facility to fight against this viral disease. In this article, a through quantitative understanding of the purine and pyrimidine spatial distribution/organization of all 89 complete sequences of SARS-CoV (available as on date in the NCBI virus database, is made using different parameters such as fractal dimension, Hurst exponent, Shannon entropy and GC content of the nucleotide sequences of the genome of SARS-CoV2. Also a cluster among all the the SARS-CoV sequences of nucleotide have been made based on their phylogeny made through their closeness (Hamming distance) based on respective purine-pyrimidine distribution.

As shown earlier, the algorithmic complexity, like Shannon information and Boltzmann entropy, tends to increase in accordance with the general law of complification. However, the algorithmic complexity of most material systems does not reach its maximum, i.e. chaotic state, due to the various laws of nature that create certain structures. The complexity of such structures is very different from the algorithmic complexity, and we intuitively feel that its maximal value should be somewhere between order and chaos. I propose a formula for calculation such structural complexity, which can be called - structuredness. The structuredness of any material system is determined by structures of three main types: stable, dissipative, and post-dissipative. The latter are defined as stable structures created by dissipative ones, directly or indirectly. Post-dissipative structures, as well as stable, can exist for an unlimited time, but at the micro level only, without energy influx. The appearance of such structures leads to the “ratchet” process, which determines the structuregenesis in non-living and, especially, in living systems. This process allows systems with post-dissipative structures to develop in the direction of maximum structuring due to the gradual accumulation of these structures, even when such structuring contradicts the general law of complification.

In the aftermath of pyroclastic-flow –dominated eruptions, lahars are the main geomorphic agent, but at the decadal scale, different sets of processes take place in the volcanic sediment cascade. At Unzen Volcano, in the Gokurakudani Gully we investigated the geomorphologic evolution and how the topographic change and the sediment change over time is controlling this transition. For this purpose, a combination of LiDAR data, aerial photography and photogrammetry, Ground Penetrating Radar and sediment grain-size analysis was done. The results show chocking zones and zones of enlargement of the gully, partly controlled by pre-eruption topography, but also by the overlapping patterns of the pyroclastic flow deposits of 1990 – 1995. The Ground Penetrating Radar revealed that on top of the typical lahar structure at the bottom of the gully, side-wall collapses were trapping finer sandy sediments formed in relatively low-energy deposition environment. This shows that secondary processes are taking place in the sediment transport process, on top of lahar activity, but also that these temporary dams may be a source of sudden sediment and water release, leading to lahars. Finally, the sediments from the gully walls are being preferentially oozed out of the pyroclastic-flow deposit, meaning that over longer period of time, there may be a lack of fines, increasing permeability and reducing internal pore-pressure needed for lahar triggering. It also poses the important question of how much of a past-event one can understand from outcrops in coarse heterometric material, as the deposit structure can remain, even after loosing part of its fine material.

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

There are introduced two new steganalytic methods not depending on the statistics of the cover objects, namely side attacks stegosystems. The first one assumes that the plaintext, encrypted before embedding, is known by the attacker. In this case, the stegosystem’s detection is based on the calculation of mutual information between message and extracted encrypted data. For this calculation, a notion of the k-nearest neighbor distance is applied. The second method is applied to HUGO, one of the most efficient steganographic algorithms. In this case the stegosystem’s detection is based on a verification of the NIST tests to the extracted encrypted messages. Moreover, we show that the problem to find a submatrix of­ the embedding matrix determining a trellis code structure in the HUGO algorithm provides a search of the stegokey of the proposed stegosystem.

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

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.

The historic western edge of bison (Bison bison) range and the ecological processes that caused its formation are frequently debated with important implications for bison restoration across North America. We test the hypothesis that a combination of bottom-up habitat suitability and top-down harvest pressure from humans were important processes in forming the western edge of bison distribution. Using 9,384 historical journal observations from 1691 – 1928, we employ MaxEnt ecological niche modelling to identify suitable bison habitat across the Western Cordillera from bottom-up climatic, land cover, and topographic factors. We then use mixed-effect logistic regression to test if bison occurrence in journal records can be in part explained by the abundance of Indigenous humans, wolves, or grizzly bears, in addition to MaxEnt-derived habitat suitability. We find support for our hypothesis because of the limited suitable habitat in the Rocky Mountains that likely prevented westward bison dispersal from core habitat, and there was a negative relationship between bison occurrence and human harvest pressure. On this basis, we propose that intensive human harvest from large populations in the Western Cordillera, subsidized by other wildlife, salmon, and vegetation resources, is an underappreciated socioecological process that needs to be restored alongside bison populations. Co-managing bison with Indigenous people will also mitigate the adverse effects of overabundant bison and maximize the ecological and cultural benefits of bison restoration.

We survey the main results emerging in the rapidly developing field that considers the geometry of thermodynamics and statistical mechanics. Our ideas of stability depend on variational principles – Maximum Entropy together with Least Action (and the isomorphic Least Exertion) – and this stability (invariance in time) indicates the centrality of the geometries of the systems. We explore a variety of examples of the application of thermodynamics in both macro- and micro-systems, and propose that irreversibility is an intrinsic and fundamental property of the physical realm (instead of being merely emergent). Using the concept of complex time, we examine the underlying mathematical unity of quantum mechanics, statistical mechanics, and geometrical thermodynamics. We show how the Planck and Boltzmann constants provide the fundamental quantum units for the phenomenological characteristics of the two Noether-conserved quantities controlling overall thermodynamic behaviour: respectively, energy and entropy production. We discuss the far-reaching isomorphisms (between all of complex time, temperature and the system symmetry) that always exist for Maximum Entropy systems, even as they exhibit either irreversible (dissipative, yet still dynamically stable) or reversible (including stable and static geometries) behaviours.

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.

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

Two extensions of the generalized double Lomax distribution are introduced - the spliced-scale generalized double Lomax distribution and the exponentiated generalized double Lomax distribution. Their properties are studied. Usefulness of the new distributions is shown by fitting them to stock returns datasets.

Experimental recordings of the collective activity of interacting spiking neurons exhibit random behavior and memory effects, thus the stochastic process modeling the spiking activity is expected to show some degree of time irreversibility. We use the thermodynamic formalism to build a framework, in the context of spike train statistics, to quantify the degree of irreversibility of any parametric maximum entropy measure under arbitrary constraints, and provide an explicit formula for the information entropy production of the inferred Markov maximum entropy process. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.

The universal Debye – Mayer – Kelly hybrid model was proposed for the description of the heat capacity from 0 K to the melting points of substance within the experimental uncertainty for the first time. To describe the heat capacity, the in-house software on the base of commercial one DELPHI-7 was used with a 95% confidence level. To demonstrate the perfect suitability of this model, a thermodynamic analysis of the heat capacities of the fourth group elements, and some compounds of the A^IIIB^V and A^IIB^VI phases was carried out. It produced good agreement within the experimental uncertainty. There is no a similar model description in literature.The Similarity Method is a convenient and effective tool for critical analysis of the heat capacities of isostructural phases, which was used as an example for diamond-like compounds. Phases with the same sum of the atomic numbers of elements (Z), such as diamond and B_0.5 N_{0.5 (cub)} (Z = 6); pure silicon (Si) and Al_0.5 P_0.5 (Z=14); pure germanium (Ge) and Ga_0.5 As_0.5 (Z = 32)); pure grey tin (alpha-Sn) and In_0.5 Sb_0.5, and Cd_0.5 Te_0.5 (Z = 50) have the same heat capacity experimental values in the solid state. The proposed models can be used to both different binary and multicomponent phases. It helps to standardize the physicochemical constants.

This study addresses the causal links between external factors and the main hydro-climatic variables. There is a gap in the literature on the description of a complete chain in addressing the structures of direct causal links of solar activity on the terrestrial variables. This is why, the present study uses the extensive facilities of the application of information theory in view of recent advances in different fields. Also, by other methods (e.g. neural networks) first are tested the existence non-linear links of solar-terrestrial influences on hydro-climate system. The results are promising related to the solar impact on terrestrial phenomena which is discriminant in space-time domain. The implications prove robust for determining the causal measure of climate variables under direct solar impact which makes it easier to consider solar activity in climate models, by appropriate parametrizations. This study found that hydro-climatic variables are sensitive to solar impact only for certain frequencies (periods) and these have a coherence with the Solar-Flux only for some lags of the Solar-Flux (in advance).

Our purpose is to address the biological problem of finding foundations of the organization in the collective activity among cell networks in the nervous system, at the meso/macroscale, giving rise to cognition and consciousness. But in doing so, we encounter another problem related to the interpretation of methods to assess the neural interactions and organization of the neurodynamics, because thermodynamic notions, which have precise meaning only under specific conditions, have been widely employed in these studies. The consequence is that apparently contradictory results appear in the literature, but these contradictions diminish upon the considerations of the specific circumstances of each experiment. After clarifying some of these controversial points and surveying some experimental results, we propose that a necessary condition for cognition/consciousness to emerge is to have available enough energy, or cellular activity; and a sufficient condition is the multiplicity of configurations in which cell networks can communicate, resulting in non-uniform energy distribution, the generation and dissipation of energy gradients due to the constant activity. These ideas may reveal possible fundamental principles of brain organization and how healthy activity may derive to pathological states.

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.

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

Supervised land-use/land-cover (LULC) classifications are typically conducted using class assignment rules derived from a set of multiclass training samples. Consequently, classification accuracy varies with the training data set and is thus associated with uncertainty. In this study, we propose a bootstrap resampling and reclassification approach that can be applied for assessing not only the uncertainty in classification results of the bootstrap-training data sets, but also the classification uncertainty of individual pixels in the study area. Two measures of pixel-specific classification uncertainty, namely the maximum class probability and Shannon entropy, were derived from the class probability vector of individual pixels and used for the identification of unclassified pixels. Unclassified pixels that are identified using the traditional chi-square threshold technique represent outliers of individual LULC classes, but they are not necessarily associated with higher classification uncertainty. By contrast, unclassified pixels identified using the equal-likelihood technique are associated with higher classification uncertainty and they mostly occur on or near the borders of different land-cover.

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

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

This paper is our attempt on the basis of physical theory to bring more clarification on the question ``What is life?'' formulated in the well-known book of Schr\"odinger in 1944. According to Schr\"odinger, the main distinguishing feature of biosystem's functioning is the ability to preserve its order structure or, in the mathematical terms, to prevent increasing of entropy. Since any biosystem is fundamentally open, it is natural to use open system's theory. However, Schr\"odinger's analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schr\"odinger should also appeal to the ambiguous notion of negative entropy. We suggest to apply the quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of the classical entropy. We consider a complex biosystem $S$ composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., $S=(S_i).$ We study the following problem: if the composed system $S$ can preserve the ``global order'' in the situation of increase of local disorder and if $S$ can preserve its entropy while some of $S_i$ increase their entropies We show that within quantum information theory the answer is positive. The significant role plays entanglement of the subsystems states. In the absence of entanglement, increasing of local disorder generates disorder increasing in the compound system $S$ (as in the classical regime).

This article analyses entropy changes triggered by specific events in deterministic and indeterministic systems. Article considers a simple model consisting of water in a cuvette, an ice cube in the device above the cuvette and a random number generator (RNG) that controls the probability of dropping the ice into water. Article introduces the entropic potential Z(T, A) of an event A occurred in a system R at the moment Т₀, which describes the influence of the event A to the entropy of the system R in the future (for the moments T>Т₀). The entropic potential of an event Z(T,A) can be calculated as the difference between the mathematical expectations of entropy of the system R for the moment T (T>Т₀) made immediately before and immediately after the event A as Z(T, A) = Ŝ_T(Т₀+dT) - Ŝ_T(Т₀-dT). Article also presents examples of calculations of the entropic potentials of events in indeterministic systems with different probabilities of events. Since real-life systems are mostly indeterministic, the entropic potentials of events in real-life usually have non-zero values. The entropic potentials of the events "useful" for the system are negative, and entropic potentials of the events "harmful" for the system are positive.

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.

Under typical marine conditions of about 80 % relative humidity, evaporation of water from the ocean is an irreversible process accompanied by entropy production. In this article, equations are derived for the latent heat of irreversible evaporation and the related non-equilibrium entropy balance at the sea surface. To achieve this, linear irreversible thermodynamics is considered in a conceptual ocean evaporation model. The equilibrium thermodynamic standard TEOS-10, the International Thermodynamic Equation of Seawater – 2010, is applied to irreversible evaporation under the assumption of local thermodynamic equilibrium. The relevance of local-equilibrium conditions for irreversible thermodynamics is briefly explained. New equations are derived for the mass flux of evaporation and for the associated non-equilibrium enthalpies and entropies. The estimated entropy production rate of ocean evaporation amounts to 0.004 W m^(-2) K^(-1) as compared to the average terrestrial global entropy production of about 1 W m^(-2) K^(-1).

We compared performance of a novel encoding Lempel-Ziv complexity (ELZC) with approximate entropy (ApEn), sample entropy (SmpEn) and permutation entropy (PerEn) as nonlinear metric to assess ECG quality. Firstly to compare performance of discerning randomness and inherent nonlinear properties within time series, this study calculated the aforementioned four nonlinear complexity values on several typical artificial time series i.e., Gauss noise, two kinds of noisy time series, two kinds of Logistic series and periodic series, respectively. Then for analyzing sensitivity of the aforementioned four complexity methods to content level of different types noise within ECG recordings, we investigated variation trend of ELZC, ApEn, SmpEn and PerEn in several synthetic ECG recordings containing different types noise (i.e., baseline wander, muscle artefacts, electrode motion, power line and mixed noise) and different signal noise ratios (i.e., 15, 10, 5, 0, −5 and −10 dB). Finally, the four complexity methods were employed to classify the quality of real ECG recordings from the PhysioNet/Computing in Cardiology Challenge 2011 (CINC 2011) of the MIT databases, then receiver operating characteristic curves (ROC) and their corresponding area under curve (AUC) were yielded. The results showed ELZC could not only distinguish randomness and chaotic within time series but also reflect content level of noise within time series, and the highest AUC of PerEn, ELZC, SmpEn and ApEn were 0.850, 0.695, 0.474 and 0.461, respectively. The results demonstrated PerEn and ELZC were more effectively than ApEn and SmpEn for assessing ECG quality.

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

Life sciences are increasingly benefiting from multidisciplinary research, combining biology, chemistry and physics. At their intersection, biothermodynamics applies the quantitative framework of thermodynamics to life processes and is a potentially interesting subject for life science students. Here a method is proposed to teach undergraduate life science students the basics of biothermodynamics, building and expanding on the concept of Gibbs energy learned as a part of the physical or general chemistry course. The discussion begins with the role of Gibbs energy as the driving force of metabolism and growth. Moreover, a biological example is proposed of the enthalpy-entropy combinations resulting in negative Gibbs energy, which should be interesting to life science students. Gibbs energy is then used to explain microorganism growth rates, using a simple thermodynamic growth model. Finally, multiplication of viruses is considered, including SARS-CoV-2, using Gibbs energy to explain the hijacking of host cell metabolism. Implementation of the proposed biothermodynamics material in classroom is discussed. The paper should be useful as material for making lectures for undergraduate students and as a starting point for anyone beginning to do research in biothermodynamics.

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.

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

We present a precise and universal method for anticipating the thermodynamic characteristics of polyatomic molecules. Unlike conventional computational approaches that rely on numerous experimental spectroscopy or calorimetry data, our model only utilizes a small number of molecular constants. We accurately predicted the values of entropy, enthalpy, specific heat, and Gibbs free energy for boron trifluoride, which were in excellent accordance with the available experimental data. This investigation introduces a new approach to deal with the anharmonic vibrations of polyatomic molecules

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.

Suppose G is a graph with vertex-orbits O1,1 O2, . . . ,Ot, and jOi j denotes the cardinallity of Oi. Then OG (x) = åt 2 i=1 xjOi j is called as orbit polynomial. It is well-known that this polynomial 3 has a unique positive zero d in the interval [0, 1]. The aim of this paper is to study the specific 4 properties of this polynomial and then we determine the location of this root for several classes of 5 complex networks to compare with other graphical measures. Besides, we compare the unique 6 positive zero measure with several well-known centrality graph measures.

In this paper, we concentrate on the study of the properties of residual Tsallis entropy for order statistics. Order statistics have an important role in reliability structural engineering for example for modelling lifetimes of series and parallel systems. The residual Tsallis entropy of ith order statistic from a continuous distribution function and its deviation from the residual Tsallis entropy of ith order statistics from a uniform distribution is investigated. In a mathematical framework, a method to express the residual Tsallis entropy of the ith order statistic from a continuous distribution in terms of the residual Tsallis entropy of the ith order statistic from a uniform distribution is provided. This approach may provide insight into the behavior and properties of the residual Tsallis entropy for order statistics. Further, we study the monotonicity properties of the residual Tsallis entropy of order statistics under dierent conditions. By studying these properties, deeper understanding of the relationship between the position of order statistics and the resulting residual Tsallis entropy is gained.

Variability is the predisposition of the elements in systems to assume different values over time and space. In biology, the variability is basic to explain differences and development in organisms but in the fields of scientific and technological information, the effects of variability on evolutionary dynamics of disciplines and technologies are unknown. In a broad analogy with the principles of biology, the variability within research fields can be a central argument to explain trajectories in scientific development and technological evolution. The purpose of the present study is to see whether statistical evidence supports the general hypothesis that the rate of growth in technologies can be explained by the level of variability in scientific fields and with this principal goal to analyze the relation between scientific variability and rate of growth in technologies. Proposed hypothesis of scientific variability here endeavors to explain basic sources of scientific development and technological evolution to lay the foundations for a general theory. The test here is based on emerging research fields of quantum technologies: Quantum Imaging, Quantum Meteorology, Quantum Sensing and Quantum Optics. A preliminary statistical evidence seems in general to support the hypothesis stated that the rate of growth in technological fields can be explained by the level of scientific variability in research fields, measured with relative entropy index. Nonparametric correlation based on Spearman’s rho shows a positive coefficient of 0.80 of these variables; linear model of the rate of technological growth = f(scientific variability) reveals a coefficient of regression equal to 1.63 (R²=0.60). Findings here suggest a general law that scientific variability positively drives scientific development and technological evolution. In particular, a higher variability within research fields can support scientific development and a high rate of growth in technological evolution (measured with scientific and technological information). Proposed hypothesis of scientific variability is especially relevant in environments of rapid change to explain determinants and dynamics of technological change within a general theoretical framework that supports technological management and forecasting of promising innovations.

With the development of computer science and software engineering, software becomes more and more complex. Traditional software reliability assurance techniques including software testing and evaluation can't ensure software reliable execution after being deployed. Software failure prediction techniques based on failure indicators can predict software failures according to abnormal indicator values. The latter can be collected using runtime monitoring techniques. An essential part of this method is finding proper indicators which have strong correlation with software failures. We propose a novel type of indicators in this work named software runtime entropy, which takes both software module execution time and call times into consideration. Three common open source software, grep, flex and gzip are used as study cases for finding the relationships between the indicators and software failures. Firstly, a series of fault injection experiments are conducted on those three software respectively. The decision tree algorithm is used to train those data to build the correlation models between software runtime entropy and software failures. Several common measures in machine learning domains such as accuracy, recall rates, and F-measure are used to evaluate the models. The decision tree models can be used as failure mechanisms to assist the failure prediction work. One can examine the value of runtime entropy and make a warning report when it ranges from the normal interval to abnormal one.

This paper proposes a reconceptualization of the hierarchical understanding of the human organism, challenging the conventional idea of the supremacy of the nervous system. We argue that symbiotic coexistence and functional interdependence among all systems provide the human body with remarkable resistance to the universal tendency of entropy. We first examine the basis of cellular life, referring to ATP and DNA, essential substances that resist the entropic tendency through complex energy mechanisms. Next, we analyze the collaboration between the body's systems, highlighting the critical role of erythrocytes, which constitute 83.9% of the total cells (24.9 trillion), in the context of energy maintenance and homeostasis. We challenge the conventional view that the nervous system, composed of neurons and glial cells, which together make up 0.6% of the total cells (0.17 trillion), occupies the apex of a biological hierarchy, arguing that the nervous system is merely a component of a broader, interdependent mechanism. Finally, we provide a detailed description of human cellular composition, emphasizing the importance of each cell type in the functional context, thus contributing to the totality of the organism. With this, we present a vigorous appeal for the realization of critical reassessments of fundamental premises in human biology.

In this paper, we will revisit the derivation of Heisenberg's uncertainty principle. We will see how the Heisenberg principle collapses at the Planck scale by introducing a minor modification. The beauty of our suggested modification is that it does not change the main equations in quantum mechanics; it only gives them a Planck scale limit where uncertainty collapses. We suspect that Einstein could have been right after all, when he stated, ``God does not throw dice." His now-famous saying was an expression of his skepticism towards the concept that quantum randomness could be the ruling force, even at the deepest levels of reality. Here we will explore the quantum realm with a fresh perspective, by re-deriving the Heisenberg principle in relation to the Planck scale. We will show how this idea also leads to an upper boundary on uncertainty, in addition to the lower boundary. These upper and lower boundaries are identical for the Planck mass particle; in fact, they are zero, and this highlights the truly unique nature of the Planck mass particle. Further, there may be a close connection between light and the Planck mass particle: In our model, the standard relativistic energy momentum relation also seems to apply to light, while in modern physics light generally stands outside the standard relativistic momentum energy relation. We will also suggest a new way to look at elementary particles, where mass and time are closely related, consistent with some of the recent work in experimental physics. Our model leads to a new time operator that does not appear to be in conflict with the Pauli objection. This indicates that both mass and momentum come in quanta, which are perfectly correlated to an internal Compton `clock' frequency in elementary particles.

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

One of the most important subjects of hydraulic engineering is the reliable estimation of the transverse distribution in rectangular channel of bed and wall shear stresses. This study makes use of the Tsallis entropy, Genetic Programming (GP) and (ANFIS) methods to assess the shear stress distribution (SSD) in rectangular channel. To evaluate the results of the Tsallis entropy, GP and ANFIS models, laboratory observations were used in which shear stress was measured using an optimized Preston tube. This is then used to measure the SSD in various aspect ratios in the rectangular channel. To investigate the shear stress percentage, 10 data series with a total of 112 different data for were used. The results of the sensitivity analysis show that the most influential parameter for the SSD in smooth rectangular channel is the dimensionless parameter B/H, Where the transverse co-ordinate is B, and the flow depth is H. With the parameters (b/B), (B/H) for the bed and (z/H), (B/H) for the wall as inputs, the modeling of the GP was better than the other one. Based on the analysis, it can be concluded that the use of GP and ANFIS algorithms is more effective in estimating shear stress in smooth rectangular channels than the Tsallis entropy-based equations.

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.

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

Bonchev and Trinajstic defined two distance based entropy measures to measure the molecular branching of molecular graphs in 1977 [Information theory, distance matrix, and molecular branching, J. Chem. Phys., 38 (1977), 4517–4533]. In this paper we use these entropy measures which are based on distance matrices of graphs. The first one is based on distribution of distances in distance matrix and the second one is based on distribution of distances in upper triangular submatrix. We obtain the two entropy measures of paths, stars, complete graphs, cycles and complete bipartite graphs. Finally we obtain the minimal trees with respect to these entropy measures with fixed diameter.

For the first time in scientific and engineering practice, it is logically and mathematically substantiated, computationally verified and metrologically confirmed that classic and quantum physics, analytical and quantum chemistry, as well as continuous symbolic and discrete digital mathematical analysis, all have computational limits of information entropy, upper 1/10^16 and lower 1/10^64. Mutual displacement of these limits relatively center of Euclidean three-dimensional and of Cartesian two-dimensional space generate sets of quantum dots of mesh topology and weighted average harmonic units of quantum metrics of internal atomic and outer cosmic space, as well as determines limits of communication speed, clock frequency, calculation power and accuracy for any computing machine with subatomic elements of memory. The matrices of functional density and entropy of energy and information fields reconciles classic and quantum physics with continuous and discrete mathematics of special and general relativity.

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.

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.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

We first of all define the arrow of time. Definition of the arrow of time will allow choosing different initial starting points. One of the issues we will also discuss is the interconnection be-tween the arrow of time, entropy and quantum information. Seth Lloyd in his 2001 work made a linkage between entropy, bits, and information via an axiomatic approach involving time in-tervals. Our take is a bit more general. We will discuss as well the t’Hooft’s statement as to in-itial conditions and times arrow, and how different cosmological models may influence initial conditions. Spoilers alert, if a nonsingular start to expansion existed, this would provide the most straightforward way to avoid a datum from classical relativity. That is, that in the actual equations of classical GR, there is no reason to have time asymmetry. Time asymmetry is built into initial conditions and we will detail several candidates. The first half of the paper brings up cosmology models and forming the arrow of time. The second is related to entropy itself and the problem of information. .

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.

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.

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.

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.

The purpose of this study is to provide an accurate formula for calculating entropy for short DNA sequences and to demonstrate how to use it to examine leukemia patient surviving. We used IDIBAPS leukemia patient’s data base with 117 anonymized records. The generalized form of the Robust Entropy Estimator (EnRE) for short DNA sequences was proposed and key EnRE futures was showed. The Survival Analysis has been done using statistical package IBM SPSS. Entropy EnRE were calculated for leukemia patients for two samples: A. 2 groups divided by median EnRE and B. 2 groups of patients were formed according to their belonging to 1st and 4th quartiles of EnRE. The result of survival analysis are statistically significant: A. p &lt; 0.05; B. p &lt; 0.005. The death hazard for a patient with EnRE below median is 1.556 times that of a patient with EnRE over median and that the death hazard for a patient of 1st quartile (lowest EnRE) is 2.143 times that of a patient of 4th quartile (highest EnRE). The transition from median to quartile patients’ groups with more EnRE differentiation confirmed the unique significance of the entropy of DNA sequences for leukemia patients surviving.

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

Different notions of entropy can be identified in different communities: (i) the thermodynamic sense, (ii) the information sense, (iii) the statistical sense, (iv) the disorder sense, and (v) the homogeneity sense. Especially the “disorder sense” and the “homogeneity sense” relate to and require the notion of space and time. One of the few prominent examples relating entropy to geometry and to space is the Bekenstein-Hawking entropy of a Black Hole. Although being developed for the description of a physics object—a black hole—having a mass, a momentum, a temperature, a charge etc. absolutely no information about these attributes of this object can eventually be found in the final formula. In contrast, the Bekenstein-Hawking entropy in its dimensionless form is a positive quantity only comprising geometric attributes like an area A—which is the area of the event horizon of the black hole-, a length L_P—which is the Planck length - and a factor ¼. A purely geometric approach towards this formula will be presented. The approach is based on a continuous 3D extension of the Heaviside function, with this extension drawing on the phase-field concept of diffuse interfaces. Entropy enters into the local, statistical description of contrast respectively gradient distributions in the transition region of the extended Heaviside function definition. The structure of the Bekenstein-Hawking formula eventually is derived for a geometric sphere based on mere geometric-statistic considerations.

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.

Artificial intelligence algorithms have gained widespread adoption in the field of air conditioning load prediction. However, their prediction accuracy is substantially influenced by the quality of training samples. Training samples that lack relevance to the predicted moments can introduce interference into the neural network's learning process, potentially leading to a state of local convergence during its iterative process. This, in turn, diminishes the robustness and generalization capabilities of the prediction model. To enhance the prediction accuracy of air conditioning load prediction models based on artificial intelligence algorithms, this study presents an artificial intelligence algorithm prediction model based on the method of sample similarity sample screening. Initially, the comprehensive similarity coefficient between samples is computed using the gray correlation analysis method, enriched with enhancements in information entropy. Subsequently, a subset of closely related samples is extracted from the original dataset and employed as the training dataset for the artificial intelligence prediction model. Finally, the trained artificial intelligence algorithm prediction model is deployed for air conditioning load prediction. The results illustrate that the method of screening training samples based on sample similarity effectively improves the prediction accuracy of BP neural network (BPNN) and extreme learning machine (ELM) prediction models. However, it is important to note that this approach may not be suitable for genetic algorithm BPNN (GABPNN) and support vector regression (SVR) models.

The introduction of exoskeletons in the industry has focused on improving worker safety. Exoskeletons have the objective of decreasing the risk of injury or fatigue when performing physically demanding tasks. The exoskeleton’s effects on the muscles is one of the most common focus in the assessments. The present study aims to analyse the muscle interactions generated by using a passive lumbar exoskeleton during load-handling tasks in laboratory conditions with and without an exoskeleton. Electromyographic data of the muscles involved in the task were recorded from twelve participants performing load-handling tasks. Correlation Coefficient, Coherence Coefficient, Mutual Information, and Multivariate Sample Entropy were calculated to determine if there were significant differences in muscle interactions between the two test conditions. Results showed statistically significant differences for all pairs of muscles and indicated that the use of the exoskeleton implied more constant values throughout the exercise. The Directed Conditional Granger Causality was obtained to study the directionality of the interactions, with significant differences in two muscle pairs Gluteus-Quadriceps and Gluteus-Lumbar in the gravity-positive direction in both cases. In conclusion, EMG parameters chosen appear to be appropriate measurements for studying the exoskeleton effects over muscle couplings.

Maximum entropy production principle (MEPP) has been formulated in the mid-twentieth century, and today it has acquired the status of an important principle of science, which is extremely effective in considering various non-equilibrium problems. In this study, for the first time, definition of life is based on an easily measurable physical quantity that is entropy production. Life and evolution are discussed from the point of view of MEPP and the Universe, but not a human

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.

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.

Chellali et al. introduced two degree concepts, ve-degree and ev-degree (Chellali et al, 2017). The ve-degree of a vertex equals to number of different edges which are incident to a vertex from the closed neighborhod of v. Moreover the ev-degree of an edge e=ab equals to the number of vertices of the union of the closed neighborhoods of a and b. The most private feature of these degree concepts is, total number of ve-degrees and total number of ev-degrees equal to first Zagreb index of the graphs for triangle-free graphs. In this paper we introduce ve-degree entropy, ev-degree entropy and investigate the relations between these entropies and the first Zagreb index entropy. Finally we obtain the maximal trees with respect to ve-degree irregularity index.

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

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.

The purpose of this work is to study the mechanism of running-in during the friction and to determine the informative parameters characterizing the degree of its completion. During the friction, contact interaction of rough surfaces causes various wave phenomena covering a wide range of frequencies, the subsequent frequency analysis can provide information about the sizes of wave sources and thereby clarify the mechanism of interaction between surface roughness. The using of the wavelet transform for processing of the signals of audible acoustic emission made it possible to determine the beginning and the end of the change in the frequency ranges of the interaction of roughness. The code developed by the authors was used to analyze the acoustic emission signals by using wavelet energy and entropy criteria. The mother wavelet was chosen by carefully evaluating the effectiveness of 54 preliminary candidates for the mother wavelet from 7 wavelet families, ac-cording to three criteria: 1) maximum wavelet energy; 2) Shannon entropy minimum; 3) maximum energy-to-Shannon entropy ratio.

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

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.

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerbly good approximation of the entanglement entropy. Finally, we show that the effectiveness of residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.

This paper presents a novel algorithm, the multi-objective nonlinear interval PageRank (MONIPR) Algorithm. This algorithm extends the conventional PageRank (PR) algorithm, integrating nonlinear interval computation and multi-objective considerations into the computation process. The MONIPR algorithm bridges a research gap in integrating nonlinear interval approaches and multi-objective problems into the PR algorithm, which were traditionally treated separately. In addition, this research adopts the constrained interval arithmetic proposed to address the limitations of the conventional PR algorithm, which tends to overlook uncertainties and results in deterministic outcomes. In addition, we use a numerical example to demonstrate the proposed algorithm, contrasting it with the conventional approaches. A numerical example demonstrates the algorithm's performance by comparing the rank intervals obtained with the traditional crisp Markov chain and PR algorithm. The results highlight the ability of the proposed algorithm to provide a range of possible rank intervals, considering both uncertainty and multi-objectives. The findings suggest potential applications in decision-making, uncertainty quantification, and systems analysis.

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

Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model, presents an intermediate vortex state when the number of possible orientations q for the system is equal to 5 or larger. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit q→∞. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.

For planetary gear has the characteristics of small volume, light weight and large transmission ratio, it is widely used in high speed and high power mechanical system. Poor working conditions result in frequent failures of planetary gear. A method is proposed for diagnosing faults in planetary gear based on permutation entropy of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) Adaptive Neuro-fuzzy Inference System (ANFIS) in this paper. The original signal is decomposed into 6 intrinsic mode functions (IMF) and residual components by CEEMDAN. Since the IMF contains the main characteristic information of planetary gear faults, time complexity of IMFs are reflected by permutation entropies to quantify the fault features. The permutation entropies of each IMF component are defined as the input of ANFIS, and its parameters and membership functions are adaptively adjusted according to training samples. Finally, the fuzzy inference rules are determined, and the optimal ANFIS is obtained. The overall recognition rate of the test sample used for ANFIS is 90.75%, and the recognition rate of gear with one missing tooth is relatively high. The recognition rates of different fault gears based on the method can also achieve better results. Therefore, the proposed method can be applied to planetary gear fault diagnosis effectively.

We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and propagating heat for networks of nonlinear oscillators. By using the Hodge decomposition of thermodynamical forces and fluxes, we derive a formula for entropy production that generalises the notion of non-potential forces and makes transparent the breaking of detailed balance and of time reversal symmetry for states arbitrarily far from equilibrium. Our formalism is then applied to describe the off-equilibrium thermodynamics of a few examples, notably a continuum ferromagnet, a network of classical spin-oscillators and the Frenkel-Kontorova model of nano friction.

Proteins in biological systems function at the interface of single molecule and bulk chemistry and thus provide novel insights into the basic physical chemistry of scaling and emergent phenomena. For example, a binary mechanical model based on the chemistry of muscle contraction unifies molecular mechanics and thermodynamics and provides an explicit solution to the Gibbs paradox. Using the same model system, here I show that chemical activities of molecular states have no effect on chemical kinetics or energetics. Specifically, while the concentration or number of molecules in a molecular state is widely thought to contribute to reaction free energies, here I show that it is not the physical presence of molecules that pushes a reaction forward but the number of microstates, , accessible in a chemical state that pulls a reaction toward equilibrium with an entropic force down an entropic funnel. With the derivation of an entropic contribution to chemical kinetics, I develop a novel chemical kinetic formulation that fully describes the chemical thermodynamics of both equilibrium and non-equilibrium reactions in terms of an a priori system reaction energy landscape.

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black holes under the generalized Brans-Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius~$r_+$~is small, the effect of the entropy correction term on the entropy is very obvious, while for larger values~$r_+$~, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of the geodesic motion of particles in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyzes the dependence of the innermost stable circular orbit on model parameters. Also, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, the specific energy and angular momentum of the particles which move in circular orbits.

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.

Tourism is an important industry that promotes national economic and social progress. All-for-one tourism is a new concept of regionally coordinated development that uses the tourism industry as an engine to boost resource integration, industrial integration, and social sharing. Tourism service is the main embodiment of cultural ecosystem services for all-for-one tourism cities. Taking Liyang in China as an example, this paper used a combination of GIS spatial analysis and big data text mining to evaluate the tourism service from three aspects: the quality of tourism resources, the comprehensiveness of tourism service facilities, and the satisfaction of tourists. The results show that (1) the tourism service is better in the northwestern and eastern areas of the city, while it is lower in the northeastern and southwestern parts; (2) the hotspot areas should focus on improving the tour routes, the transport capacity, and excessive charges; the cold spot areas should work on ecological restoration and creating new tourism attractions by combining the local industries; (3) rural tourism integrating agriculture and visitation should be highlighted as a key growth point to improve the city’s tourism service function.

For more than one hundred years, scientists dispute the correct interpretation of Lorentz transformations within the framework of the special theory of relativity of Albert Einstein. On the one hand, the changes in length, time and mass with increasing velocity are interpreted as apparent due to the observer dependence within special relativity. On the other hand, real changes are described corresponding to the experimental evidence of mass increase in particle accelerators or of clock delay. This ambiguity is accompanied by an ongoing controversy about valid Lorentz-transformed thermodynamic quantities such as entropy, pressure and temperature. In this paper is shown that the interpretation problem of the Lorentz transformations is genuinely anchored within the postulates of special relativity and can be solved on the basis of the thermodynamic approach of matter-energy equivalence, i.e. an energetic distinction between matter and mass. It is suggested that the velocity-dependent changes in state quantities are real in each case, in full agreement with the experimental evidence.

We consider that the relationship between entropy in statistical mechanics, which is the Boltzmann principle, and the complex velocity potential in complex fluid dynamics. We define the generalized complex entropy which expanded entropy from real space to complex space. We show that the complex entropy can be expressed by the composition of sources, sinks and laminar flows of the complex velocity potential. Therefore, the complex entropy is considered a special case of the complex fluid dynamics,that is, the complex velocity potential. In other words, we show that the complex entropy is expressed by the complex velocity potential. Moreover, we show that a complex number is expressed by the complex entropy. Thus, we show that the complex velocity potential is expressed by the complex entropy. Namely, we will expand entropy to complex space and see that the complex entropy is expressed by the complex velocity potential. Furthermore, we examine the possibility that it is an expansion of Boltzmann's principle and Planck distribution.

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

Market uncertainty has a significant impact on market performance. Previous studies put much efforts in investigations on market uncertainty related to information asymmetry and risk. However, they have neglected the uncertainty inherent in market transactions, which is also an important aspect of market performance, besides quantity of transactions and market efficiency. In this paper, we put forward the concept of transaction entropy to measure the market uncertainty and see how it changes with price. The definition of transaction entropy is the ratio of total information entropy of all traders to quantity of transactions, reflecting the level of uncertainty in making transactions. And the transaction entropy is the lowest at equilibrium, it will be decreasing in a shortage market, and increasing in a surplus market. Additionally, we make a comparison of total entropy of the centralized market with that of the decentralized market, revealing that the price filtering mechanism could effectively reduce market uncertainty. Overall, the introduction of transaction entropy enriches our understanding of market uncertainty and facilitates a more comprehensive assessment of market performance.

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.

(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.

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.

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

Background: This study aimed to investigate how external perturbations caused by the treadmill belt's acceleration (Acc) and deceleration (Dec) during the Initial Contact (Initial), Mid Stance (Mid) and Pre-Swing (ToeOff) phase affect gait regularity in young adults. Methods: Twenty-one healthy young females walked on a treadmill in a virtual environment (Grail, Motek), where four unexpected perturbations were applied to the left belt at Initial, Mid, and ToeOff. Sample Entropy (SampEn) was calculated for the center of mass (CoM) displacements, for six perturbation scenarios in three directions: anterior-posterior (AP), medial-lateral (ML), and vertical (vert), with SampEn vector lengths (m) ranging from 2 to 10. Results: The CoM displacement exhibited its highest regularity (low SampEn values) in the AP and vert-directions during Dec_ToeOff, across all m values. Similarly, this pattern was observed in the ML-direction, but exclusively for m = 2 and 4. The least regular CoM trajectories (high SampEn values) were for Dec_Mid in the AP-direction, across all m values. This trend persisted in the ML-direction, only for m = 2 and 4. However, the most irregular CoM displacements in the ML-direction occurred during Dec_ToeOff for the remaining m values. Vertical CoM displacements exhibited the highest irregularities during Dec_Initial for m ≥ 4. Conclusions: Evaluating the regularity of CoM displacements using SampEn can be a useful tool for assessing how gait perturbations are handled.

In this review, our goal is to design and test quantum-like algorithms for Artificial Intelligence (AI) in open systems to structure a human-machine team to be able to reach its maximum performance. Unlike the laboratory, in open systems, teams face complexity, uncertainty and conflict. All task domains have complexity levels, some have low, and others high levels. Complexity in this new domain is affected by the environment and the task, which are both affected by uncertainty and conflict. We contrast the individual and interdependence approaches to teams. The traditional and individual approach focuses on building teams and systems by aggregating the best available information for individuals, their thoughts, behaviors and skills. Its concepts are characterized chiefly by one-to-one relations between mind and body, a summation of disembodied individual mental and physical attributes, and degrees of freedom corresponding to the number of members in a team; however, this approach is characterized by the many researchers who have invested in it for almost a century with few effects that can be generalized to human-machine interactions; by the replication crisis of today (e.g., the invalid scales for self-esteem, implicit racism, and honesty); and by its many disembodied concepts. In contrast, our approach is based on the quantum-like nature of interdependence. It allows us to theorize about the bistability of mind and body, but it proposes a measurement problem and a non-factorable nature. Bistability addresses team structure and performance; the measurement problem solves the replication crisis; and the non-factorable aspect of teams reduces the degrees of freedom and the information derivable from teammates to match findings by the National Academies of Science. We begin with a review of the science of teams and a focus on human-machine team research in the laboratory versus the open; justifications for rejecting traditional social science while supporting our approach; a full understand of the complexity of the domain, tasks in the domain, and how teams address both; the mathematics involved; a review of results from our model versus the open field; a discussion of the results; conclusions; and the path forward to successfully advance the science of interdependence and autonomy.

This article introduces a new fractional approach to the concept of information dimension of complex networks, based on a (q,q′)-entropy proposed in the literature. The q parameter measures how far is the number of subsystems (for a given size ε) from the mean number of overall sizes. The q′ (interaction index) measures when the interactions between subsystems are greater (q′&gt;1), lesser (q′&lt;1) or equal to the interactions into these subsystems. The computations of the proposed information dimension are carried out on several real-world and synthetic complex networks. The results from the proposed information dimension are compared with those from the information dimension based on the Shannon entropy.

The relationship of the animal with its environment has been of longstanding interest in philosophy and science. Here I provide a brief introduction to concepts that place an emphasis on mutualism as the basis of organism - environment interaction, in contrast to the long standing view that the environment exerts an instrumental role in shaping the organism. Two influential theories have been von Uexküll’s theory of umwelt and Gibson’s theory of affordances. The former envisioned the animal as immersed in its surroundings (umwelt) to form a functional unit. In a similar manner, the latter theory describes a unity between 1) environmental information that provides the animal with opportunities for action (affordances) and 2) the ability of the animal to perceive and engage with those affordances. These views have influenced more recent ecological models of the organism as the functional unit of biology and have also influenced models of immune function. In ecological models, agency is seen as the ability of the organism to predict and control its engagement with the environment in order to maintain its integrity. The predominant contemporary model of neural function in which perception and action are understood to operate through Bayes-like active inference complements the concept of agency as proposed by the mutualism models. However, it is suggested that rather than a constant mutualism, encounters between organism and environment range over a dynamic spectrum from dualism to mutualism. It is also suggested that along this spectrum, agency emerges when the balance of instrumentality shifts from the environment to the organism, and that the balance of this relationship can further progress towards a felicitous mutualism. Meaning emerges between environmental information and an agent as opportunity for action. Implications for opportunities to foster agency in animals within our care is noted.

Wolfenden and his coworkers observed the astronomical numbers for the catalytic proficiency of some enzymes. We connected that pinnacle of biological evolution to the universal thermodynamic evolution. We added or multiplied a random noise with chosen rate constants to explore the correlation between dissipation and enzyme efficiency for ten enzymes: beta-galactosidase, glucose isomerase, β-lactamases from three bacterial strains, ketosteroid isomerase, triosephosphate isomerase, and carbonic anhydrase I, II, and T200H. The turnover number kcat and catalytic efficiency kcat/KM are proportional to the overall entropy production – the main parameter from irreversible thermodynamics. For most enzymes with the Michaelis-Menten type cycle kinetics, the best increase in the forward kcat/KM follows after increasing the equilibrium constant of substrate-enzyme association. The Discussion section emphasizes the role of biological evolution in harvesting order (high enzyme efficiency) from disorder (high noise and dissipation). It also connects the applications of the maximum partial entropy production theorem in optimizing enzyme kinetics (D. Juretić "Bioenergetics - A Bridge across Life and Universe") with the present total entropy production role analysis. De novo enzyme design and various attempts to speed up the rate-limiting catalytic steps may profit from our theoretical insights.

In this paper, we will extend the expected value of the function w.r.t the uniform probability measure on sets measurable in the Caratheodory sense to be finite for a larger class of functions, since the set of all measurable functions with infinite or undefined expected values forms a prevalent subset of the set of all measurable functions, which means "almost all" measurable functions have infinite or undefined expected values. Before we define the specific problem in section 2, we will outline some preliminary definitions. We'll then define the specific problem (along with a partial solution in section 3) to visualize the complete solution. Along the way, we will ask a series of questions to clarify our understanding of the paper.