Entropy is a concept derived from Physics that has been used to describe natural and social systems’ structure and behaviour. Applications of the concept in the social sciences so far have been largely limited to the disciplines of economics and sociology. In the current paper the concept of entropy is applied to organizational citizenship behaviour with implications for urban organizational sustainability. A heuristic is presented for analysing personal and organizational citizenship configurations and distributions within a given workforce that can lead to corporate entropy; and for allowing prescriptive remedial steps to be taken to manage the process should entropy from this source threaten its sustainability and survival.

It is shown that the Lambda component in the cosmological Lambda-CDM model can be conceived as vacuum energy, consisting of gravitational particles subject to Heisenberg’s energy-time uncertainty. These particles can be modelled as elementary polarisable Dirac-type dipoles (“darks”) in a fluidal space at thermodynamic equilibrium, with spins that are subject to the Bekenstein-Hawking entropy. Around the baryonic kernels, uniformly distributed in the universe, the spins are polarized, thereby invoking an increase of the effective gravitational strength of the kernels. It explains the dark matter effect to the extent that the numerical value of Milgrom’s acceleration constant can be assessed by theory. Non-polarized vacuum particles beyond the baryonic kernels compose the dark energy. The result is a quantum mechanical interpretation of gravity in terms of quantitatively established shares in baryonic matter, dark matter and dark energy, which correspond with the values of the Lambda-CDM model..

Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems—thermal, externally loaded, internally reactive, open and closed––are developed via selection of suitable thermodynamic potentials. Here we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented––and demonstrated on grease degradation, battery charging and discharging, metal fatigue and pump flow––can be used for design, analysis, and support of diagnostic monitoring and optimization.

Iterated games, in which the same economic interaction is repeatedly played between the same agents, are an important framework for understanding the effectiveness of strategic choices over time. To date very little work has applied information theory to the information sets used by agents in order to decide what action to take next in such strategic situations. This article looks at the mutual information between previous game states and an agent's next action by introducing two new classes of games: ’invertible games’ and ‘cyclical games'. By explicitly expanding out the mutual information between past states and the next action we show under what circumstances these expressions can be simplified. These information measures are then applied to the Traveler's Dilemma game and the Prisoner's Dilemma game, the Prisoner's Dilemma being invertible, to illustrate their use. In the Prisoner's Dilemma a novel connection is made between the computational principles of logic gates and both the structure of games and the agents' decision strategies. This approach is applied to the cyclical game Matching Pennies to analyse the foundations of a behavioural ambiguity between two well studied strategies: ‘Tit-for-Tat' and ’Win-Stay, Lose-Switch'.

The model of an oscillating universe proposed by A. Friedmann in 1922 dominated cosmology for a long time. R. Tolman put forward a thermodynamic argument against the cyclic cosmological model, believing that entropy should accumulate from cycle to cycle. J. Bekenstein and S. Hawking discovered a tremendous amount of entropy associated with black holes. This discovery led to the conclusion that the majority of the Universe's entropy is contained in black holes. N. Poplawski considers a Universe that oscillates within a black hole. This paper analyzes the relationship between the entropy of black holes and the oscillating Universe inside a large black hole. It is demonstrated that the entropy of a black hole can only be defined for an external observer. For an observer inside the black hole, its entropy is zero. This opens up the possibility of constructing a cyclic cosmology in which entropy and the size of the visible part of the Universe change strictly periodically. This does not violate the second law of thermodynamics because the continuous accumulation of entropy from cycle to cycle pertains to the surface of the big black hole, which is invisible to the internal observer.

The anisotropy in the CMBR detected by the COBE satellite has sprouted the research and theories of the void that got created, after being washed away by a parallel universe after its collision. This details of the roadmap to the parallel universe, that are previously been entangled, but now, separated, with the concept of 2-time dimensions as a time curve of containing the closed curves embedded on the surface area, thereby time running backward in orientation in the parallel universe, along with the perspective of eternal inflation and divided subspaces giving birth to twin universes are provided here. This time curve being responsible for creating an exponentiality of time frames, growing in layers, giving us the perception of the confabulations being an indication of the previously connected worlds.

Coarse-grained molecular dynamics simulations are employed to investigate the spatiotemporal evolution of vesicles (polymersomes) by the self-assembly of randomly distributed amphiphilic BAB triblock copolymers with hydrophilic A and hydrophobic B blocks in an aqueous solution. The vesiculation pathway consists of several intermediate structures, such as an interconnected network of copolymer aggregates, a cage of cylindrical micelles and a lamellar cage. The cage-to-vesicle transition occurs at a constant aggregation number and practically eliminates the hydrophobic interfacial area between the B block and solvent. Molecular reorganization under-lying the sequence of morphology transitions from a cage-like aggregate to a vesicle is nearly isentropic. The end-to-end distances of isolated copolymer chains in solution and those within a vesicular assembly follow log normal probability distributions. This is attributed to the pre-ponderance of folded chain configurations in which the two hydrophobic end groups of a given chain stay close to each other. However, the probability distribution of end-to-end distances is broader for chains within the vesicle as compared to that of a single chain. This is due to the swelling of the folded configurations within the hydrophobic bilayer. Increasing the hydropho-bicity of the B block reduces the vesiculation time without qualitatively altering the self-assembly pathway.

The temperature effect plays an important role for an accurate determination of the polar free energy, polar thermodynamic parameters, and enthalpic and entropic Lewis’s acid base properties of oxides, polymers and composites polymers/oxides. The adsorption of polymers on other solid surfaces is crucial in many industrial applications, coatings, paints, catalysis, colloids and adhesion processes. (1) Background: Inverse gas chromatography at infinite was used for the physico-chemical characterization of solid substrates by determining the thermodynamic parameters of adsorption of model organic solvents on solid surfaces such as polymers, metallic oxides, carbon fibers, pharmaceutical or 3D/4D printing substrates. (2) Methods: A new method based on the London dispersion equation was applied with a new parameter associating the deformation po-larizability and the harmonic mean of the ionization energies of solvent. More accurate values of the dispersive and polar interaction energies of the various organic solvents adsorbed on PMMA in bulk phase and PMMA/silica at different recovery fractions were obtained as well as the Lewis acid-base parameters and the transition temperatures of the different composites. (3) Results: This new methodology gave very interesting results on the behavior of PMMA adsorbed on silica. An important effect of the temperature and the recovery fraction on the various physicochemical and thermodynamic properties was highlighted. The variations of all interaction parameters showed the presence of three transition temperatures for the different PMMA adsorbed on silica with the various coverage rates with a shift of these temperatures for a recovery fraction of 31% (4) Con-clusions: An important variation of the polar enthalpy and entropy of adsorption, the Lewis ac-id-base parameters and the intermolecular separation distance as a function of the temperature and the recovery fraction of PMMA on silica.

During the last years some new variants of Permutation entropy have been introduced and applied to EEG analysis, among them a conditional variant and variants using some additional metric information or being based on entropies different from the Shannon entropy. In some situations it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.

It is shown that the Lambda component in the cosmological Lambda-CDM model can be conceived as vacuum energy, consisting of gravitational particles subject to Heisenberg’s energy-time uncertainty. These particles can be modelled as elementary polarisable Dirac-type dipoles (“darks”) in a fluidal space at thermodynamic equilibrium, with spins that are subject to the Bekenstein-Hawking entropy. Around the baryonic kernels, uniformly distributed in the universe, the spins are polarized, thereby invoking an increase of the effective gravitational strength of the kernels. It explains the dark matter effect of galaxies to the extent that a numerical value of Milgrom’s acceleration constant can be assigned by theory. Non-polarized vacuum particles beyond the baryonic kernels compose the dark energy at the cosmological level. The result is an interpretation of gravity at the quantum level in terms of quantitatively established shares in baryonic matter, dark matter and dark energy, which correspond with the values of the Lambda-CDM model.

Ontological premises have profound theoretical implications. This analysis posits a single, universal structure composed of two ontic entities: discrete, quantized units of space ("Planck Spheres") and a State of Absolute Nothingness (the "SOAN"). Planck Spheres and the SOAN form a physical, ultra-high (3 x N) dimensional space ("Planck Space") and a discrete 3D space (or "4D spacetime"). Together, Planck Space and 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the "Dual Ontology"). Critically, a one-to-one mapping and identity exists between the Planck Spheres comprising 4D spacetime and Planck Space. The Dual Ontology conjecture supports radically simplified physical explanations for three distinct areas of theoretical physics: First, the conjecture reconciles fundamental issues in Special Relativity and quantum mechanics by explaining why single and N-body quantum states (a) dynamically evolve in 4D spacetime subject to the speed of light and (b) instantaneously collapse in a physical Planck Space that is not subject to Special Relativity. Second, the temporal and physical asymmetry between the dynamic evolution of quantum states in 4D spacetime subject to Special Relativity and the instantaneous collapse of quantum states in a Planck Space where Special Relativity is inapplicable explains quantum path irreversibility and the arrow of time. Third, at or near the heat death of 4D spacetime, the instantaneous collapse of the energy content of Planck Space and the simultaneous transition of 4D spacetime's extremely widely dispersed energy content to a non-singular, generally localized volume at t = 0 explains 4D spacetime's isotropy, homogeneity, extremely high energy, pressure, and temperature, flatness, and low gravitational entropy. It also explains the horizon and fine-tuning problems.

In order to solve the problem of feature extraction of underwater acoustic signals in complex ocean environment, a new method for feature extraction from ship radiated noise is presented based on empirical mode decomposition theory and permutation entropy. It analyzes the separability for permutation entropies of the intrinsic mode functions of three types of ship radiated noise signals, and discusses the permutation entropy of the intrinsic mode function with the highest energy. In this study, ship radiated noise signals measured from three types of ships are decomposed into a set of intrinsic mode functions with empirical mode decomposition method. Then, the permutation entropies of all intrinsic mode functions are calculated with appropriate parameters. The permutation entropies are obviously different in the intrinsic mode functions with the highest energy, thus, the permutation entropy of the intrinsic mode function with the highest energy is regarded as a new characteristic parameter to extract the feature of ship radiated noise. After that, the characteristic parameters, namely, the energy difference between high and low frequency, permutation entropy, and multi-scale permutation entropy, are compared with the permutation entropy of the intrinsic mode function with the highest energy. It is discovered that the four characteristic parameters are at the same level for similar ships, however, there are differences in the parameters for different types of ships. The results demonstrate that the permutation entropy of the intrinsic mode function with the highest energy is better in separability as the characteristic parameter than the other three parameters by comparing their fluctuation ranges and the average values of the four characteristic parameters. Hence, the feature of ship radiated noise can be extracted efficiently with the method.

This article systematically disproves the notion that entropy is a measure of disorder and disproves Schrödinger's notion of negative entropy (negentropy) using multiple novel and compelling arguments. To mathematically describe the second law of thermodynamics, the concept of entropy was created and defined in the 1860s as heat energy divided by thermodynamic temperature, and the entropy of an object increases when it absorbs heat. This is the uncontroversial and fundamental nature of entropy, which is pivotal to current thermodynamics and from which multiple facts are deduced. These facts consistently disprove the above two widely accepted notions. Multiple biological facts (e.g., life orderliness is encoded and provided by inherited genes rather than entropy decline) can also disprove Schrödinger's negentropy notion. This article further elucidates the reasoning errors of the two notions. Moreover, the second law of thermodynamics and the notion that many natural or social systems tend to become more disordered over time result from distinct statistical probabilities and are hence independent of each other.

This paper proposes that intelligent processes can be completely explained by thermodynamic principles. They can equally be described by information-theoretic principles that, from the standpoint of the required optimizations, are functionally equivalent. The underlying theory arises from two axioms regarding distinguishability and causality. Their consequence is a theory of computation that applies to the only two kinds of physical processes possible—those that reconstruct the past and those that control the future. Dissipative physical processes fall into the first class, whereas intelligent ones comprise the second. The first kind of process is exothermic and the latter is endothermic. Similarly, the first process dumps entropy and energy to its environment, whereas the second reduces entropy while requiring energy to operate. It is shown that high intelligence efficiency and high energy efficiency are synonymous. The theory suggests the usefulness of developing a new computing paradigm called Thermodynamic Computing to engineer intelligent processes. The described engineering formalism for the design of thermodynamic computers is a hybrid combination of information theory and thermodynamics. Elements of the engineering formalism are introduced in the reverse-engineer of a cortical neuron. The cortical neuron provides perhaps the simplest and most insightful example of a thermodynamic computer possible. It can be seen as a basic building block for constructing more intelligent thermodynamic circuits.

A simple line of reasoning, based on the most fundamental concepts of thermodynamics, yields some intriguing results for a better understanding of the processes occurring in the observable Universe. Gravitational mass must be continuously generated within an expanding thermodynamic system for this system to remain closed. The Second Law is a direct consequence of this production of mass. Simple expressions for the entropy and temperature of the Universe were obtained and the results agree well with observable values. Furthermore, it is demonstrated that the conservation laws within the Universe are independent of its energy density. Based on the solution for the quantum state of the Universe, it is conjectured that the Second Law is incomplete and must be complemented to a conservation law, which takes into account the growth of the amount of information within the Universe. Once the Second Law is complemented to a conservation law, the importance of mass generation within the Universe becomes well pronounced – not only gravitational effects play the role of an organising force, but also the amount of mass within the Universe defines both the amount of information within the Universe and the level of the Universe’s complexity.

Numerous scientific fields employ entropy, the Shannonian measure of disorder and inaccessible information. Current paper examines educational uses of entropy. The major objectives of this survey are to create a coherent perspective of the applicability of classical entropies and to provide a concise detailed explanation that blends technical pertinence with conceptual extraction from the most recent literature. What's more intriguing are the closing thoughts mixed with a few unsolved issues and the creation of a future work schedule in these areas.

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

The present work investigates primarily the morphology evolution of the body-centered-cubic (BCC)/B2 phases in AlxNiCoFeCr high-entropy alloys (HEAs) with increasing Al content, which has been neglected so far. There exist two types of microscopic morphologies of BCC and B2 phases in this HEA series: one is the weave-like morphology induced by the spinodal decomposition, and the other is the microstructure of a spherical disordered BCC precipitation on the ordered B2 matrix that appears in HEAs with a much higher Al content. The shape of coherent precipitates is found to be closely related to the lattice misfit between BCC and B2 phases, which is sensitive to Al. The mechanical properties, including the compressive yielding strength and microhardness of the AlxNiCoFeCr HEAs, are also discussed in light of the concept of the valence electron concentration (VEC).

Two heating surfaces with longitudinal fins are located within the closed channel inside the housing made of thermal insulation material. The air flow inside the channel was carried out by an axial fan. The heating of the fins is established by using two positive temperature coefficient heating elements (PTC). Air flows circularly from one finned surface to another, and after reaching the required temperature, it leaves the housing. In the heating system conceived in this way, a methodology based on transient thermal irreversibility of heating sources and circular air flow has been established. Volumetric air flow and circulation time within the channel were varied. The total entropy generated does not include hydraulic irreversibility, but transient thermal irreversibility of the air and heat sources. For conducting analytical modeling, the temperature of the PTC heater was considered constant at 423K and 473K. Volumetric air flow varied in the interval from 0.00001m3s-1 to 0.00006m3s-1. The experimental determination of the transient thermal entropy was performed at a much higher air flow rate of 0.005m3s-1 inside the closed channel. Due to the continuous increase in air temperature, the temperatures of both PTC heaters increased within the examined time interval of 300s. According to experimental testing, the total transient thermal entropy of the described heating system has a minimum after 175s from the start of the circular heating of the air. The minimum of transient entropy also implies the optimal time of channel opening and exit of heated air.

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

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

Predicting the outcome of a future game between two National Basketball Association (NBA) teams poses a challenging problem of interest to statistical scientists as well as the general public. In this article, we formalize the problem of predicting the game results as a classification problem and apply the principle of maximum entropy to construct NBA maximum entropy (NBAME) model that fits to discrete statistics for NBA games, and then predict the outcomes of NBA playoffs by the NBAME model. The best NBAME model is able to correctly predict the winning team 74.4 percent of the time as compared to some other machine learning algorithms which is correct 69.3 percent of the time.

CoCrFeNiMn high-entropy alloy coatings were prepared on compacted graphite iron（CGI） through plasma cladding to strength the CGI substrate. The effects of heat treatment temperatures and times on the microstructure and mechanical properties of the CoCrFeNiMn coatings were investigated. After heat treatment, a single FCC phase was remained in the coating as compared to the deposited one, with smaller dendrites, larger dendritic spacing and more Cr-rich compounds precipitated between dendrites. The coatings’ microhardness was increased after heat treatment. After heat treated at 660°C for 90 minutes, the coating had the highest microhardness of 563±6.9 HV0.2, the lowest frictional coefficient of 0.71 and the smallest wear mass loss of 1.12 mg, and it had the best wear resistance.

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

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

In the current complex and uncertain macroeconomic situation, improving the inherent resilience of the new energy vehicle industry chain is the key to effectively addressing various risks and challenges, and achieving dynamic balance between high-quality industrial development and industrial chain security. Based on the basic concept of resilience and the actual situation of new energy vehicle industry chain development, this study constructs a comprehensive evaluation index system for the resilience of the new energy vehicle industry chain, which includes four dimensional first-level indicators of coping resistance, adaptive resilience, autonomous control and leading competitiveness. In addition, it is measured by combining the data related to the new energy vehicle industry chain in Changzhou City. Our study shows that the situation on the new energy vehicle industry chain is complicated, and the comprehensive evaluation index system is more favorable for evaluating its resilience level.

To enhance the applicability of dual-phase high-entropy alloys (HEAs) like Fe32Cr33Ni29Al3Ti3, fabricated via selective laser melting (SLM), a focus on improving their mechanical properties is essential. As part of this effort, heat treatment was explored. This study compares the microstructure and mechanical properties of the as-printed sample with those cooled in water after undergoing heat treatment at temperatures ranging from 1000 to 1200 ℃ for 1 hour. Both pre- and post-treatment samples reveal a dual-phase microstructure comprising FCC and BCC phases. Although heat treatment led to a reduction in tensile and yield strength, it significantly increased ductility compared to the as-printed sample. This strength-ductility trade-off is related to changes in grain sizes with ultrafine grains enhancing strength and micron grains optimizing ductility, also the influence of the content of FCC/BCC phases and dislocation density. In particular, the sample heat-treated at 1000 °C for 1 hour and then water-cooled exhibited a better combination of strength and ductility, a yield strength of 790 MPa, and an elongation of 13%. This research offers innovative perspectives on crafting dual-phase HEA of Fe32Cr33Ni29Al3Ti3, allowing for tailorable microstructure and mechanical properties through a synergistic approach involving SLM and heat treatment.

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method to classify spatiotemporal processes based on entropy measurements. To test and validate the method, we selected four classes of similar processes related to the evolution of random patterns: dynamic colored noises ((i)~white and (ii)~red); (iii)~weak turbulence from reaction-diffusion; (iv)~hydrodynamic fully developed turbulence, and (v)~plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon Permutation Entropy ($S^p_H$) and a new approach based on Tsallis Spectral Permutation Entropy ($S^s_q$). Notably, our observations reveal the segregation of reaction terms in this $S^p_H \times S^s_q$ space, a result that identifies specific sectors for each class of dynamic process, and can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.

China's economic development has shifted from high speed to high quality. This study constructs an evaluation index for China’s high-quality development utilizing a new development concept. The entropy method and cluster analysis were used to assess the level of high-quality development in China between 2015 and 2021. Kernel density estimation method was employed to explore spatiotemporal dynamics. The results reveal significant differences in the level of economic development among provinces in China; the eastern region is significantly better than the central, northeastern, and western regions. From the perspective of the sub-item evaluation, challenges with uneven, uncoordinated, and insufficient economic development exist in various Chinese provinces.

It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the ‘probability assumption’ needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann’s Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.

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

Recently, there has been growing interest in alternative measures of uncertainty, including cumulative residual entropy. In this paper, we consider a mixed system consisting of n components, assuming that all components are operational at time t. We use the system signature to calculate the cumulative residual entropy of the mixed system’s remaining lifetime. This measure is a useful criterion for assessing the predictability of a system’s lifetime. We study several results related to the cumulative residual entropy of mixed systems, including expressions, limits, and order properties. These results shed light on the behavior of the measure and provide insights into the predictability of mixed systems. In addition, we propose a criterion for selecting a preferred system based on the relative residual cumulative entropy. This criterion is closely related to the parallel system and provides a practical way to choose the best system configuration. Overall, the present study of cumulative residual entropy and the proposed selection criterion provide valuable insights into the predictability of mixed systems and can be applied in various fields.

The real systems are often complex, nonlinear, and noisy in various areas including mathematics, natural science, and social science. We present the symplectic entropy (SymEn) measure as well as an analysis method based on SymEn to estimate the nonlinearity of the complex system by analyzing the given time series. The SymEn estimation is a kind of entropy based on symplectic principal component analysis (SPCA) which represent organized but unpredictable behaviors of systems. The key to SPCA is to preserve the global submanifold geometrical properties of the systems through symplectic transform in the phase space, which is a kind of the measure-preserving transforms. The capability of preserving the global geometrical characteristics makes the SymEn a test statistic to detect the nonlinear characteristics in several typical chaotic time series and the stochastic characteristic in the Gaussian white noise. The results are in agreement with findings in the approximate entropy (ApEn), the sample entropy (SampEn) and the fuzzy entropy (FuzzyEn). Moreover, the SymEn method is also used to analyze the nonlinearities of the real signals (including the EEG signals for ASD and healthy subjects, and the sound and vibration signals for the mechanical systems). The results indicate that the SymEn estimation can be taken as a measure for describing the nonlinear characteristics in the data collected from the natural complex systems.

In a vacuum tube two identical and parallel Ag-O-Cs emitters A and B (work function 0.8eV) ceaselessly emit thermal electrons at room temperature. The thermal electrons are controlled by a static uniform magnetic field so that the number of electrons migrate from A to B exceeds the one from B to A (or vice versa). The net migration of thermal electrons from A to B quickly results in a charge distribution of A charged positively and B negatively, and a potential difference between A and B emerges, enabling a continuous output current and a stable power to an external load (e.g., a resistor). Thus, the tube cools down (slightly). The (slightly) cooled tube extracts heat from ambient air, and all the heat is converted into electric energy without other effect. We believe the experiment is in contradiction to the Kelvin statement of the second law.

The choice associated with words is a fundamental property of natural languages. It lies at the heart of quantitative linguistics, computational linguistics, and language sciences more generally. Information-theory gives us tools at hand to measure precisely the average amount of choice associated with words—the word entropy. Here we use three parallel corpora—encompassing ca. 450 million words in 1916 texts and 1259 languages—to tackle some of the major conceptual and practical problems of word entropy estimation: dependence on text size, register, style and estimation method, as well as non-independence of words in co-text. We present three main results: 1) a text size of 50K tokens is sufficient for word entropies to stabilize throughout the text, 2) across languages of the world, word entropies display a unimodal distribution that is skewed to the right. This suggests that there is a trade-off between the learnability and expressivity of words across languages of the world. 3) There is a strong linear relationship between unigram entropies and entropy rates, suggesting that they are inherently linked. We discuss the implications of these results for studying the diversity and evolution of languages from an information-theoretic point of view.

Quantum physics is intrinsically probabilistic. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such state. The degrees of freedom of a quantum state are position and spin, and upon their specification Born's rule in phase space defines randomness. We focus on the spin degree of freedom and elucidate the spin entropy. Then, we present some of its properties and show how entanglement increases spin entropy. Some speculative predictions on the decay of the $Z^0,W^{+,-}$ gauge bosons conclude the paper.

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

The philosophy of testing statistical hypothesis is a natural consequence and functional extension of mathematical analysis of Probability. Along with the concept of recurrence when applied to random sequences and functions, it leads to the analysis of a priori and posterior which implies testing statistical hypothesis. Testing statistical hypothesis also involves algebraic, functional and dimensional considerations, which are found in the works of Laplace. Aspects of mathematical analysis such as universality of solutions, Laws of Large Numbers, Entropy, Information, and various functional dependencies are the main factors explained in the five properties that lead to implication of testing statistical hypothesis. Various interesting examples with modern scientific significance from genetics, astrophysics, and other areas give methodological access to answers of different problems and phenomena which are involved in the logic of testing statistical hypothesis.

We study the atom-field interaction at finite temperature and in the dispersive regime. We show that the master equation for this sytem may be solved with the use of superoperator techniques. We calculate the linear entropy in case the field is initially in a coherent state and the atom in a superposition of its ground and excited states.

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

The physical roots, interpretation, controversies and precise meaning of the Landauer Principle are surveyed. Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surrounding. The Landauer Principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin limit and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decrease in a temperature of a thermal bath will decrease the energy consumption of a single computation, but, in parallel, it will slow the computation. The Landauer principle bridges between John Archibald Wheeler “it from bit” paradigm and thermodynamics. Experimental verifications of the Landauer Principle are surveyed. Interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to the quantum and non-equilibrium systems is addressed. Landauer Principle represents the powerful heuristic principle bridging the physics, information theory and computer engineering.

In the current scenario, liver abnormalities are one of the most serious public health concerns. Cirrhosis of the liver is one of the foremost causes of demise from liver diseases. To accurately predict the status of liver cirrhosis, physicians frequently use automated computer-aided approaches. In this paper the clustering techniques like Fuzzy C Means (FCM), Possibilistic Fuzzy C Means (PFCM), Possibilistic C Means (PCM), Sample Entropy features are extracted from normal and cirrhotic liver ultrasonic Images. The extracted features are classified as normal and Cirrhosis one through Gaussian Mixture Model(GMM), Softmax Dis(SDC), Harmonic Search Algorithm (HSA), SVM(Linear), SVM(RBF), SVM(Polynomial), Artificial Algae Optimization (AAO) and hybrid classifier Artificial Algae Optimization (AAO) with Gaussian Mixture Mode (GMM). The classifiers performances are compared based on Accuracy, F1 Score, MCC, F Measure, Error rate and Jaccard metric (JM).The hybrid classifier AAO GMM with PFCM feature outperforms than other classifiers and attained an accuracy of 99.03 % with MCC of 0.90

In this paper, the Shannon entropy measure was used to assess changes in precipitation and temperature conditions. Due to the short, low-volume sequences of precipitation and temperature data analysed, a bootstrap method was used in the procedure for calculating Shannon entropy. The analysis used minimum and maximum values of monthly precipitation totals and monthly mean temperatures for 377 catchments distributed across the globe. A 110-year data series from 1901 to 2010 was analysed. Entropy values for the estimated parameters of the generalised extreme value distribution (GEV) were calculated for the adopted data. Entropy value calculations were performed for the left-hand constraint, based on minimum values, and for the right-hand constraint, based on maximum values. The applicability of Shannon's entropy measure in the analysis of climate change was demonstrated by allowing the degree of disorder and complexity of the distributions describing climate variables in the form of precipitation and temperature to be measured. This made it possible to obtain information on the directions of changes occurring with regard to minimum and maximum values in the field of monthly precipitation and mean temperatures in the analysed catchments. The study demonstrated the existence of Shannon entropy trends. The evaluation of entropy trends for precipitation and temperature sequences was performed using non-parametric tests. Mann -Kendall tests at the 5% significance level were used for trend analyses. The Pettitt test was performed to determine the point of change in trend for the rainfall and temperature data. The performed analysis was supported by graphical presentations.

Static standing postural stability has been measured by multiscale entropy (MSE), which is used to measure complexity. In this study, we used the average entropy (AE) to measure the static standing postural stability, as AE is a good measure of disorder. The center of pressure (COP) trajectories were collected from 11 subjects under four kinds of balance situation, from stable to unstable: bipedal with open eyes, bipedal with closed eyes, unipedal with open eyes, and unipedal with closed eyes. The AE, entropy of entropy (EoE), and MSE methods were used to analyze these COP data, and EoE was found to be a good measure of complexity. The AE of the 11 subjects sequentially increased by 100%as the balance situations progressed from stable to unstable, but the results of EoE and MSE did not follow this trend. Therefore, AE, rather than EoE or MSE, is a good measure of static standing postural stability. Furthermore, the comparison of EoE and AE plots exhibited an inverted U curve, which is another example of a complexity versus disorder inverted U curve.

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

The fractal dimension of is identified in this paper. More importantly, the undertaken research has shown how affects the Koch snowflake . The study has demonstrated the existence of negative values of (Koch snowflake), which connects to a considerable number of extremely intriguing mathematical and physical research areas. The information-theoretic impact on the Sierpiniski Gasket dimension , which corresponds to , was treated in a more fundamental way. Notably, the credibility of this current study adds to the existing kThe fractal dimension of is identified in this paper. More importantly, the undertaken research has shown how affects the Koch snowflake . The study has demonstrated the existence of negative values of (Koch snowflake), which connects to a considerable number of extremely intriguing mathematical and physical research areas. The information-theoretic impact on the Sierpiniski Gasket dimension , which corresponds to , was treated in a more fundamental way. Notably, the credibility of this current study adds to the existing knowledge for the information- theoretic fractal dimensions. On another applicative note, this paper offers some potential applications of fractal dimension to smart cities. The investigation of the threshold theorems for and in terms of the triad is part of the next study phase. Additionally, investigating the newly obtained 's corresponding arbitrary Sierpinski Gasket for the first time.applicative note, this paper offers some potential applications of fractal dimension to smart cities. The investigation of the threshold theorems for and in terms of the triad is part of the next study phase. Additionally, investigating the newly obtained 's corresponding arbitrary Sierpinski Gasket for the first time.

The fundamental objective is to study the application of multivariate sets of data in Gaussian distribution. This paper examines broad measurements of structure for both Gaussian and non-Gaussian distributions, which shows that they can be described in terms of the infor-mation-theoretic between the given covariance matrix and correlated random variables (in terms of relative entropy). In order to develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion supported by illustrations, both technically and statistically. The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic's science and implementations. It also helps readers grasp the themes' fundamental concepts. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis based on differential equations, a wide range of information is addressed, including basic to application concerns.

This paper seeks to explore some of the issues to be welcomed but also warned against in general but also specified from an illustrative sample of ‘smart’ projects that caused outcomes that were neither ‘smart’ nor ‘resilient’. These give pointers to a ‘thirdspace’ as a descriptor of the most advanced application of sustainability thinking regarding relational spatial development planning. This contribution examines difficulties in delivering both ‘smart’ and ‘resilient’ responses of interest or value to citizens confronted with recurring crises that derive directly or with implications for sustainability issues. Identified are constraints and issues acting as obstacles to governance, management ‘layering’ and ‘learning’ causing failures of many weak or never-delivered projects. Critiques of static, or worse ‘magical’ thinking are increasingly invoked in consequence. In the analysis of ‘live cases’ all these problems showed up ‘in real life’. The author was pleased that his mentor, the late UCLA planning theorist Ed Soja’s application of the idea of ‘Thirdspace’ received prescient vindication from the results of this adjudication.

For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure.

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

The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the correlation is often strongly non-linear. To understand this complex dependence, we consider the classical Brownian diffusion in this work. Under certain rational assumption, i.e. in the bi-component fluid mixture, the mass of the Brownian particle $M$ is far greater than that of the bath molecule $m$, we can adopt the weakly couple limit. Only considering the first-order approximation of the mass ratio $m/M$, we obtain a linear motion equation in the reference frame of the observer as a Brownian particle. Based on this equivalent equation, we get the Hamiltonian at equilibrium. Finally, using canonical ensemble method, we define a new entropy that is similar to the Kolmogorov-Sinai entropy. Further, we present an analytic expression of the relationship between the diffusion coefficient $D$ and the entropy $S$ in the thermal equilibrium, that is to say, $D =\frac{\hbar}{eM} \exp{[S/(k_Bd)]}$, where $d$ is the dimension of the space, $k_B$ the Boltzmann constant, $\hbar $ the reduced Planck constant and $e$ the Euler number. This kind of scaling relation has been well-known and well-tested since the similar one for single component is firstly derived by Rosenfeld with the expansion of volume ratio.

In this paper, the elemental construct of an I-shaped fin cooling a heat generating volume is studied through the entropy production perspective. Using the constructal design method framework with entropy production minimization as an objective leads to different optimal shape ratio, different from the ones obtained using the excess of temperature. Moreover, the optimal shape ratio evolution is not necessary the same for local entropy production minimization (excess of entropy production) and global entropy production (entropy produced in the whole area). Finally, an analysis on a possible dimensionless number is introduced for the study of constructal plates.

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

It has been recognized for some time that even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel-Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.

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

The paper explores the Kullback-Leibler divergence formalism (KLDF) applied to the stable MG1 queue manifold. More potentially, both service time probability and cumulative functions which make KLDF exact are obtained. The credibility of KLDF is justified through consistency axioms. Some potential applications of Kullback-Leibler divergence to Biometry are presented. The paper concludes with closing remarks combined with some challenging open problems and the next phase of research.

In this work, satellite data from the Clouds and Earth’s Radiant Energy System (CERES) and Moderate Resolution Imaging Spectroradiometer (MODIS) instruments is analyzed to determine how the global absorbed sunlight and global entropy generation rate have changed during the time period from 2002 to 2023. The data is used to test hypotheses derived from the Maximum Power Principle (MPP) and Maximum Entropy Production Principle (MEP) about the evolution of earth’s surface and atmosphere. The results indicate that the amount of absorbed sunlight has increased over the last 20 years but rising surface temperatures have caused the entropy generation rate to remain approximately constant despite that decrease in albedo. The results are simpler to explain using the MPP but do not completely rule out the MEP. Given the acceptance of the MPP or MEP, some extensions and nuances are discussed.

The numerical simulation of entropy generation at mixed natural free and forced convection flow in a square lid-driven cavity filled with an eletrically conducting binary fluids saturated porous media in the presence of a magnetic field is performed in this investigation. Both the top and bottom horizontal walls of the cavity are kept at constant and different temperatures while the left and right vertical walls are adiabatic and insulated. The magnetic field is applied in normal direction to the cavity. The Darcy model, including Brinkman term relative to viscous effects and Forchheimer term due to inertial forces, is used for the momentum equations, and the SIMPLER algorithm, based on the control volume finite-element method approach is used to solve the pressure –velocity coupling. The flow pattern and the heat transfer characteristics inside the cavity are presented in the form of isotherms, streamlines and isentropic lines and average Nusselt number trend. The entropy generation rate is determined for various values of Darcy number (10^-3 ≤ Da ≤ 1) and for a range of Hartmann number (0 ≤ Ha ≤ 10²). This study is limited to Pr = 7 which corresponds to water. It is observed that entropy generation is very affected by the variations of dimensionless control parameters considered.

The Rényi entropy functional was optimised for the novel findings of this investigation under various conditions. Their research's findings suggest that the complete spectrum of Lévy stable distributions is covered by generalised t-distributions. Additionally, an exposition was undertaken to prove that the Lévy distribution generalizes Tsallisian distribution, rather than the reverse. The current study is a strong generalization of an existing research work in the literature.

During the last 50 years, an interdisciplinary approach in research in various scientific fields has become widely spread. This process significantly deepens and widens our scientific knowledge, but on the other hand makes more difficult choosing a discipline to be used by students and young researchers. The dynamic development of science makes this choice even harder. There is a widely spread opinion that thermodynamics uses a rigorous mathematical apparatus. This paper describes that knowledge of the fundamental principles of thermodynamics is required for deep understanding of crucial biological processes. Thus the effort put into learning classical and nonequilibrium thermodynamics does not make harder, but easier gaining a better knowledge of biological processes. This essay is an attempt to convey personal experience in using thermodynamics to describe biological systems and processes they perform.

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

The utilization of selective laser melting (SLM) for high entropy alloys (HEAs) holds significant promise in commercial applications, and substantial experimental research efforts have been directed toward this domain. To take advantage of the reported experimental data of SLM manufactured (SLM-ed) HEAs and reduce unnecessary experimentation, this study incorporates machine learning (ML) techniques for the phase and tensile properties prediction of SLM-ed HEAs, thus presenting a novel avenue for accelerating the discovery of new SLM-ed HEAs. Through the adjustment of material descriptors and machine learning models, a model has been developed with an impressive accuracy of 93.8% in distinguishing between face-centered cubic (FCC), body-centered cubic (BCC), and dual-phase (FCC+BCC). Additionally, optimized models have been devised for the prediction of tensile properties, namely ultimate tensile strength (UTS), yield strength (YS), and elongation (δ), achieving noteworthy MAPEs (mean absolute percentage errors) of 10.33%, 8.55%, and 28.48%, respectively. Furthermore, several HEAs were fabricated using SLM, and the experimental outcomes exhibited a favorable alignment with the predicted results. These efforts carry significant implications in advancing the utilization of SLM for HEAs.

Models with age as a variable but actual dynamics invariant under age structure allow use of MaxEnt to predict uniform age structure. Interpretations include a major role for accepting randomness as a causal principle in ecology (in the face of ignorance, in a further interpretative stance).

We study different aspects of an exactly solvable master equation (ME). Its simplicity allows one direct access to the details of its workings, highlighting significant features and peculiarities. The existence of phase transitions is unveiled.

The calculation of the standard enthalpies of vaporization, sublimation and solvation of organic molecules is presented using a common computer algorithm on the basis of a group-additivity method. The same algorithm is also shown to enable the calculation of their entropy of fusion as well as the total phase-change entropy of liquid crystals. The present method is based on the complete break-down of the molecules into their constituting atoms and their immediate neighbourhood; the respective calculations of the contribution of the atomic groups by means of the Gauss-Seidel fitting method is based on experimental data collected from literature. The feasibility of the calculations for each of the mentioned descriptors was verified by means of a 10-fold cross-validation procedure proving the good to high quality of the predicted values for the three mentioned enthalpies and for the entropy of fusion, whereas the predictive quality for the total phase-change entropy of liquid crystals was poor. The goodness of fit (Q²) and the standard deviation (σ) of the cross-validation calculations for the five descriptors was as follows: 0.9641 and 4.56 kJ/mol (N=3386 test molecules) for the enthalpy of vaporization, 0.8657 and 11.39 kJ/mol (N=1791) for the enthalpy of sublimation, 0.9546 and 4.34 kJ/mol (N=373) for the enthalpy of solvation, 0.8727 and 17.93 J/mol/K (N=2637) for the entropy of fusion and 0.5804 and 32.79 J/mol/K (N=2643) for the total phase-change entropy of liquid crystals. The large discrepancy between the results of the two closely related entropies is discussed in detail. Molecules, for which both the standard enthalpies of vaporization and sublimation were calculable, enabled the estimation of their standard enthalpy of fusion by simple subtraction of the former from the latter enthalpy. For 990 of them the experimental enthalpy-of-fusion values are also known, allowing their comparison with predictions, yielding a correlation coefficient R² of 0.6066.

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

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

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

This study examined the association between pressure injuries and complexity of abdominal temperature measured in residents of a nursing facility. The temperature served as a proxy measure for skin thermoregulation. Refined multiscale sample entropy and bubble entropy were used to measure the complexity of the temperature time series measured over two days at 1-minute intervals. Robust summary measures were derived for the multiscale entropies and used in predictive models for pressure injuries that were built with adaptive lasso regression and neural networks. Both types of entropies were lower in the group of participants with pressure injuries (n=11) relative to the group of non-injured participants (n=15). This was generally true at the longer temporal scales, with the effect peaking at scale τ=23 minutes. Predictive models for pressure injury on the basis of refined multiscale sample entropy and bubble entropy yielded 92% accuracy, outperforming predictions based on any single measure of entropy. Combining entropy measures with a widely used risk assessment score led to the best prediction accuracy. Complexity of abdominal temperature series could therefore serve as an indicator of risk of pressure injury.

This paper is devoted to change-point detection using only the ordinal structure of a time series. A statistic based on the conditional entropy of ordinal patterns characterizing the local up and down in a time series is introduced and investigated. The statistic requires only minimal a priori information on given data and shows good performance in numerical experiments.

In this paper, we propose a method for assessing the effectiveness of entropy features using several chaotic mappings. We anlyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) on four discrete mappings: the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn is shown to have improved global efficiency (GEFMCC) in the classification task compared to NNetEn. At the same time, there are local areas of the time series dynamics in which the classification efficiency NNetEn is higher than FuzzyEn. The results of using horizontal visibility graphs (HVG) instead of the raw time series are also shown. GEFMCC decreases after HVG time series transformation, but there are local areas of the time series dynamics in which the classification efficiency increases after including the HVG. The scientific community can use the results to explore the efficiency of entropy-based classification of time series.

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

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

Properties of coherent states for the Heisenberg group over a field of $p$-adic numbers are investigated. It turns out that coherent states form an orthonormal basis. The family of all such bases is parametrized by a set of self-dual lattices in the phase space. The Wehrl entropy $S_W$ is considered and its properties are investigated. In particular, it is proved that $S_W\geq 0$ and vanishes only on coherent states. For a pair of different bases of coherent states, an entropic uncertainty relation is obtained. It is shown that the lower bound for the sum of the corresponding Wehrl entropies is given by the distance between the lattices. The proof uses the fact that the bases of coherent states corresponding to a pair of lattices are mutually unbiased.

Quantum mechanics introduces the concept of an observer who selects a measuring device and reads the outputs. This measurement process is irreversible. Lately, scholars on quantum collapse phenomena have presented a quantum-like formalism describing the measurement results as an interpretation of the measured object. Note that an observer must read the interpretation results after the interpretation process. Therefore, we propose that the definition of the concept of life should be expanded based on the following concept: A living system decreases entropy, measured results are interpreted, and an internal observer reads the commentary.

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

The purpose of this study is to check out the involvement of entropy in Mpemba effect. Provided that preheating of the water the cooling duration is reduced, we theoretically show that water gains more entropy when warmed and re-cooled to the original temperature.

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.

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

The issue of monitoring and early warning of rock instability has received increasing critical attention in the study of rock engineering. To investigate the damage evolution process of granite under triaxial compression tests, acoustic emission (AE) tests were performed simultaneously. This study firstly introduced two novel parameters, i.e., the coefficient of variation (CoV) of the information entropy and correlation dimension of the amplitude data from the AE tests, to identify the precursor of the failure of granite. Then the relationship between the changes in these parameters and the stress-time curve was compared and analyzed. The results of this study show that: (1) There is a strong correlation between the CoV of the information entropy and the failure process of granite. The granite failed when the CoV curve raised to a plateau. (2) The fluctuation of the correlation dimension indicates the different stages of the loading process, i.e., the initial compaction stage, the linear elastic stage, the yield stage, and the failure stage. Each stage contains a descending and a rising process in the correlation dimension curve, which indicates that this parameter could be used to identify the precursor of the failure as well. (3) The combined analysis of the two can improve the accuracy of rock instability prediction. This study provides new insights into the prediction of rock instability, which has theoretical implications for the stability of subsurface engineering rock masses.

In this paper, we present a technique to unify the Reissner–Nordstr¨om metric and the Kerr–Newman metric. We construct a specifific model and calculate the entanglement entropy of black horizon. We are interested in the entangled particle and antiparticle spinning on the black hole horizon. The two Reissner-Nordstr¨om horizons r±, are the results of the rotation of several entangled particle-antiparticle on the real horizon. The energy absorbed by a black hole is transformed into a kinetic energy of the entangled particle-antiparticles. This study provides a new type of black hole metric. We show that the rotation of an entangled system of a particle and an antiparticle can create a extremal black hole. We also explore some of the implications of this point of view for the black hole entanglement.

The historical idea of entropy as a property of a body has been reviewed and shown to arise from Clausius’s view of heat as motion. This view of heat, being intermediate between the now defunct idea of heat as substance and the modern view that heat represents an exchange of energy, implied that a body contains a definite quantity of heat. Heat, and therefore entropy, was thus considered a property of a body. These ideas led Clausius to develop his famous inequality and the idea that entropy always increases in irreversible, non-cyclic processes. In this paper, the notion of the entropy as a property of a body is examined in detail. A physical meaning is attached to the thermodynamic entropy by showing that a change in the function Q/T can be understood as representing a change in the number of ways that energy can be distributed among the degrees of freedom active in the system at any given temperature. The idea is illustrated with reference to solids and simple liquids. It is shown that the total thermodynamic entropy is, in general, less than the Boltzmann entropy, except for the case of a monatomic classical ideal gas in which the number of degrees of freedom is independent of temperature. Finally, entropy as a state function is discussed. It is argued that this is entirely mathematical in nature and that the entropy of a state represented in p-V space is not equivalent to a physical property of a physical system in the same thermodynamic state.

A method for studying properties of the earth's surface tremor, measured by means of GPS, is proposed. Four characteristics of tremor are considered: the entropy of the distribution of wavelet coefficients, the Donoho-Johnston wavelet index, and two estimates of the spectral slope. The anomalous areas of tremor are determined by estimating the probability densities of extreme values of the studied properties. The criteria for abnormal tremor behavior are based on the proximity to, or the difference between, tremor properties and white noise. The greatest deviation from the properties of white noise is characterized by entropy minima and spectral slope and DJ index maxima. This behavior of the tremor is called "active". The "passive" tremor behavior is characterized by the maximum proximity to the properties of white noise. The principal components approach provides weighted averaged density maps of these 2 variants of extreme distributions of parameters in a sliding time window of 3 years are considered. Singular points are the points of maximum average densities. The method is applied to the analysis of daily time series from a GPS network in the West USA in 2009-2022. It turned out that singular points of tremor form well-defined clusters.

A method for studying properties of the earth's surface tremor, measured by means of GPS, is proposed. Four characteristics of tremor are considered: the entropy of the distribution of wavelet coefficients, the Donoho-Johnston wavelet index, and two estimates of the spectral slope. The anomalous areas of tremor are determined by estimating the probability densities of extreme values of the studied properties. The criteria for abnormal tremor behavior are based on the proximity to, or the difference between, tremor properties and white noise. The greatest deviation from the properties of white noise is characterized by entropy minima and spectral slope and DJ index maxima. This behavior of the tremor is called "active". The "passive" tremor behavior is characterized by the maximum proximity to the properties of white noise. The principal components approach provides weighted averaged density maps of these 2 variants of extreme distributions of parameters in a sliding time window of 3 years are considered. Singular points are the points of maximum average densities. The method is applied to the analysis of daily time series from a GPS network in the West USA in 2009-2022. It turned out that singular points of tremor form well-defined clusters.

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

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

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc. A link is available for downloading an Excel program which calculates the degree of dependence of two events in a sample space with equally likely outcomes.

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

Contrary to previous belief, mutation frequency also depends on how essential a gene is. Mutation frequency is substantially lower in the coding regions of essential genes and higher in less essential genes. Even though the mutation bias based on gene essentiality is incapable of invalidating Darwinism, this bias certainly added a rather unsubtle obstacle to it by contradicting a paradigm that was widely held: that mutations are random in the sense of being independent of their function for the organism. The reason this bias occurs is currently unknown. Here, I present the theoretical solution of why genetic mutations also depend on whether the gene is more or less essential. My theory is that each gene or epigene has its own level of resistance to entropic elevation, something directly proportional to the frequency of its expression. The more a gene is expressed, the higher is its resistance to entropic elevation and vice versa. For genetic information to be conserved instead of suffering mutation, a relevant factor is also the frequency of its expression. The energy expenditure directed to a gene of current utility engenders resistance to entropic elevation of the information encoded in that gene, as energy enables not only the existence of information but also its conservation. My theory—which is based on fundamental physics and contains predictions that can be empirically tested—solves a crucial problem in evolutionary biology and genetics; if I am right, I will have established a biological law.

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

The thermocontextual interpretation (TCI) establishes a system’s exergy, entropic energy, and thermal entropy as thermocontextual properties of state, defined with respect to its positive temperature surroundings. This work extends previous applications of the TCI to irreversible and statistical transitions. The TCI defines statistical entropy as a transactional process of derandomization and transition to a negative-entropy state. Statistical measurements of a confined quantum particle’s position are detailed in terms of reversible processes of instantiation and actualization. The TCI then formalizes the MaxEnt as a fundamental physical principle. We apply MaxEnt and statistical entropy measurements to the double-slit experiment. Particles passing through parallel slits record a wave interference pattern, but a “which-slit” detector eliminates wave interference. Richard Feynman called the double-slit experiment the only mystery, at the heart of quantum mechanics. The TCI offers a simple explanation. The which-slit detector breaks the system’s symmetry, enabling particles to pass through one slit or the other, and MaxEnt selects the asymmetrical transition, which has no wave interference and a higher statistical entropy.

Synergy, emerges from synchronized reciprocal positive feedback loops between a network of diverse actors. For this process to proceed, compatible information from different sources synchronically coordinates the actions of the actors resulting in a nonlinear increase in the useful work or potential energy the system can manage. In contrast noise is produced when incompatible information is mixed. This synergy produced from the coordination of different agents achieves non-linear gains in free energy and in information (negentropy) that are greater than the sum of the parts. The final product of new synergies is an increase in individual autonomy of an organism that achieves increased emancipation from the environment with increases in productivity, efficiency, capacity for flexibility, self-regulation and self-control of behavior through a synchronized division of ever more specialized labor. Examples that provide quantitative data for this phenomenon are presented. Results show that increases in free energy density require decreases in entropy density. This is proposed as a law of thermodynamics.

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

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

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

In this paper, we study the relativistic correction to Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann-Gibbs(BG) statistics with its relativistic generalization, Kaniadakis statistics, or κ-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable only in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the κ → 0 limit.

We address the unsolved question of how best to estimate the collision entropy, also called quadratic or second order Rényi entropy. Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at their valid estimates starting from experimental data, so to derive suitable classification methods for the underlying processes, but optimal solutions have not been reached yet. Limited to the estimation of collision entropy, a one-line formula is presented here. The results of some specific Monte Carlo experiments give evidence of the validity of this estimator even for the very low densities of the data spread in high-dimensional sample spaces. The method strengths are unbiased consistency, generality and minimum computational cost.

This paper presents a quantitative approach to poetry, based on the use of several statistical measures (entropy, informational energy, N-gram, etc.) applied to a few characteristic English writings. We found that English language changes its entropy as time passes, and that entropy depends on the language used and on the author. In order to compare two similar texts, we were able to introduce a statistical method to asses the information entropy between two texts. We also introduced a method of computing the average information conveyed by a group of letters about the next letter in the text. We found a formula for computing the Shannon language entropy and we introduced the concept of N-gram informational energy of a poetry. We also constructed a neural network, which is able to generate Byron-type poetry and to analyze the information proximity to the genuine Byron poetry.

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

This study is framed on the Information Theory as a constructive criterion to generate probabilistic distributions –through the elaboration of Bayesian Networks- and to reduce the uncertainty in the occurrence and relationship between two key psychological variables associated with the sports’ performance: Self-Determined Motivation and Competitive Anxiety. We analyzed 674 universitary students/athletes who competed in the 2017 Universitary Games (Universiade) in México, from 44 universities, with an average age of 21 years old (SD = 2.07), and with a sportive experience of 8.61 years of average (SD = 5.15). Methods: Regarding the data analysis, first of all a CHAID algorithm was carried out for to know the independence links among variables, and then two Bayesian networks (BN) were elaborated. The validation of the BN revealed AUC values ranging from 0.5 to 0.92. Subsequently, various instantations were carried out with hypothetical values applied to the “bottom” variables. Results showed two probability trees that have Extrinisic Motivation and Amotivation at the top, while the anxiety/activation due to the worry for performance was at the bottom of probabilities. The instantiations carried out support the existence of these probabilistic relationships, demonstrating the little influence on the competition anxiety generated by the intrinsic motivation. In conclusion, the reduction of the uncertainty made up by the restricted BN may aloe to re-introduce Information Theory principles in psychosocial studies, allowing authors to obtain useful probabilities values upon target psychological variables related with sportive performance.