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

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

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

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

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

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

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

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

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.

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.

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

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

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.

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.

In recent years, vision-centric perception has played a crucial role in autonomous driving tasks, encompassing functions such as 3D detection, map construction, and motion forecasting. However, the deployment of vision-centric approaches in practical scenarios is hindered by substantial latency, often deviating significantly from the outcomes achieved through offline training. This disparity arises from the fact that conventional benchmarks for autonomous driving perception predominantly conduct offline evaluations, thereby largely overlooking the latency concerns prevalent in real-world deployment. While a few benchmarks have been proposed to address this limitation by introducing effective evaluation methods for online perception, they do not adequately consider the intricacies introduced by the complexity of input information streams. To address this gap, we propose the Autonomous-driving Streaming I/O (ASIO) benchmark, aiming to assess the streaming inputs characteristics and online performance of vision-centric perception in autonomous driving. To facilitate this evaluation across diverse streaming inputs, we initially establish a dataset based on the CARLA Leaderboard. In alignment with real-world deployment considerations, we further develop evaluation metrics based on information complexity specifically tailored for streaming inputs and streaming performance. Experimental results indicate significant variations in model performance and ranking under different major camera deployments, underscoring the necessity of thoroughly accounting for the influences of model latency and streaming inputs characteristics during real-world deployment. To enhance streaming performance consistently across distinct streaming inputs features, we introduce a backbone switcher based on the identified streaming inputs characteristics. Experimental validation demonstrates its efficacy in perpetually improving streaming performance across varying streaming inputs features.

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

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.

A CoCrFeNiNb0.65 eutectic high-entropy alloys (EHEAs) prepared by arc melting were irradiated with a 100 keV He+ ion beam. Swelling, helium bubbles and mechanical response induced by irradiation were evaluated. When the ion fluence reached 1.0×1018 ions/cm2, the irradiation-induced swelling occurred on the sample surface, and as the ion fluence increasing, the swelling became increasingly severe and the surface of Nb-rich phase appeared peeling and shedding. Meanwhile, along the boundaries of matrix and Nb-rich phase there was a neat line of helium bubbles. The size of these helium bubbles decreased with distance from the center of the helium bubble layer. This result indicated that the phase boundaries were favorable sites for the nucleation and gathering of helium bubbles. Nanoindentaion results indicated that hardening and softening induced by He+ ion irradiation occurred in various ion fluences. At ion fluence of 5.0×1017 ions/cm2, the CoCrFeNiNb0.65 EHEAs exhibited an obvious hardening behavior, which can be explained by dislocation-dominated hardening effect. When the ion fluence reached 1.0×1018 ions/cm2 and 2.0×1018 ions/cm2, the hardening effect decreased probably due to the helium bubble aggregation and growth, as well as helium bubbles induced noncompact structures. The results of this study provide insights into the effect of helium bubbles on mechanical evolution and pave the way for designing EHEAs suitable for the nuclear industry.

We consider an $N$ fermion system at low temperature $T$ in which we encounter special particle number values $N_m$ exhibiting special traits. These values arise in focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all $N$-values, but experience sudden jumps at the $N_m$. For a quantum state described by the matrix $\rho$, its purity is expressed by $Tr \rho^2$ and then the degree of mixture is given by $1 - Tr \rho^2$, a quantity that coincides with the entropy $S_q$ for $q=2$. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity . Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systemsn that are usually manipulated at zero temperature. Here we wish to study the subject at finite temperature. Gibbs' ensemble is appealed to. Some interesting insights are thereby gained.

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

In this paper, a Markov random field model is proposed to determine a site’s light pollution risk level. The specific data of 12 indicators of five typical cities in China is first collected to establish a hierarchical indicator system using an R-type clustering algorithm. Then, the entropy weight method is used to filter, determine 10-factor indicators, three potential impact indicators, and a light pollution risk index, and establish an undirected probability map model. A light pollution measurement based on Markov random field is obtained, and a location-based light pollution risk assessment index (LBLPRAI) is proposed. LBLPRAI of different types of sites is analyzed, and three possible intervention strategies are proposed to solve the light pollution problem: road lighting system planning, increasing vegetation coverage, and building system planning. Finally, the simulated annealing algorithm is used to determine the best intervention strategy, and it is concluded that the use of strategy 1 in the urban community 2 is the most effective measure, which can reduce the risk level of light pollution by 17.2%.

Rice farming households having limited capital do various combinations of the capital to get diversified livelihoods in continuing their lives. The purpose of this study was to analyze the effect of the household capital of rice farmers on livelihood diversification in Indramayu District. Survey method with data sources from 214 rice farming households taken by proportional simple random sampling technique. Data analysis used the partial least square method. The results found that the household capital of rice farmers has a positive and significant effect on the livelihood diversification. Government policy recommendations were determined in order of priority are physical capital with the help of agricultural tools and machinery, natural capital by anticipating climate change, financial capital by increasing support for capital sources, social capital by social networks, and human capital by improving farming skills.

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

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

In this paper we consider the congruence problem that arises in the post-analysis of Bayesian network models reconstructed from different datasets. Apart from the structure, a typical network numerically encodes relationship intensities, assigning numerical score to network edges via the scoring criterion used in the reconstruction process. This scoring is rarely a directly interpretable quantity with proper units of measure and an absolute scale, and often comes short in desirable characteristics of a true metric. This leads to poor portability of edge magnitude considerations between similar networks, originating from different sources. In this work, we address this problem by estimating the effect that data-specific resolution limit has on conditional independence, as reflected by information-theoretic entropy, and by the appropriate modification of MDL score, which removes the inconsistency between the score components in both the meaning and units. We also numerically validate our findings and expose additional performance advantages obtained via this modification.

A thermodynamic description of nano-porous media must handle the size- and shape-dependence of the media properties. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course grained scale, applying Hill's thermodynamics for small systems to the subsystems. we argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to di¤erences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation- dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of porous media permeabilities. Practical possibilities are further discussed.

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

Complex biological systems consist of large numbers of interconnected units, characterized by emergent properties such as collective computation. In spite of all the progress in the last decade, we still lack a deep understanding of how these properties arise from the coupling between the structure and dynamics. Here, we introduce the multiscale emergent functional state, which can be represented as a network where links encode the flow exchange between the nodes, calculated using diffusion processes on top of the network. We analyze the emergent functional state to study the distribution of the flow among components of 92 fungal networks, identifying their functional modules at different scales and, more importantly, demonstrating the importance of functional modules for information content of networks, quantified in terms of network spectral entropy. Our results suggest that the topological complexity of fungal networks guarantees the existence of functional modules at different scales keeping the information entropy, and functional diversity, high.

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].

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

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

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

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

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

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

Let f : V → V be a Cohomological Expanding Mapping¹ of a smooth complex compact homogeneous manifold with $ dim_{\mathbb{C}}(\Vc)=k \ge 1$ and Kodaira Dimension $\leq 0$. We study the dynamics of such mapping from a probabilistic point of view, that is, we describe the asymptotic behavior of the orbit $ O_{h} (x) = \{h^{n} (x), n \in \mathbb{N} \quad \mbox{or}\quad \mathbb{Z}\}$ of a generic point. Using pluripotential methods, we have constructed in our previous paper \cite{Armand4} a natural invariant canonical probability measure of maximal Cohomological Entropy $ \nu_{h} $ such that ${\chi_{2l}^{-m}} (h^m)^\ast \Omega \to \nu_h \qquad \mbox{as} \quad m\to\infty$ for each smooth probability measure $\Omega $ in $\Vc$ . We have also studied the main stochastic properties of $ \nu_{h}$ and have shown that $ \nu_{h}$ is a smooth equilibrium measure , ergodic, mixing, K-mixing, exponential-mixing. In this paper we are interested on equidistribution problems and we show in particular that $ \nu_{h}$ reflects a property of equidistribution of periodic points by setting out the Third and Fourth Main Results in our study. Finally we conjecture that $$\nu_h:=T_l^+ \wedge T_{k-l}^-,$$ $$\dim_\HH(\nu_h)= \Psi h_{\chi}(h) , $$ $$\dim_\HH( \mbox{Supp} T_l^+) \geq 2(k-l) + \frac{\log \chi_{2l}}{\psi_l},$$ $$|\langle \nu_m^x-\nu_h,\zeta\rangle|\leq M \Big[1+\log^+{1\over D(x,\Tc)}\Big]^{\beta/2}\|\zeta\|_{\Cc^\beta} \gamma^{-\beta m/2}$$ and $$|\langle \nu_m^x-\nu_h,\zeta\rangle|\leq M \Big[1 +\log^+{1\over D(x,E_\gamma)}\Big]^{\beta/2}\|\zeta\|_{\Cc^\beta} \gamma^{-\beta m/2}.$$

Let $f:V\rightarrow V $ be a Cohomological Expanding Mapping¹ of a smooth complex compact homogeneous manifold with dim_C(V) = k ≥ 1 and Kodaira Dimension $\leq 0$. We study the dynamics of such mapping from a probabilistic point of view, that is, we describe the asymptotic behavior of the orbit $ O_{f} (x) = \{f^{n} (x), n \in \mathbb{N} \quad \mbox{or}\quad \mathbb{Z}\}$ of a generic point. Using pluripotential methods, we construct a natural invariant canonical probability measure of maximum Cohomological Entropy $ \mu_{f} $ such that ${\chi_{2l}^{-m}} (f^m)^\ast \Omega \to \mu_f \qquad \mbox{as} \quad m\to\infty$ for each smooth probability measure $\Omega $ on V . Then we study the main stochastic properties of $ \mu_{f}$ and show that $ \mu_{f}$ is a measure of equilibrium, smooth, ergodic, mixing, K-mixing, exponential-mixing and the unique measure with maximum Cohomological Entropy. We also conjectured that $\mu_f:=T_l^+ \wedge T_{k-l}^-$, $\dim_\H(\mu_f)= \Psi h_{\chi}(f) $ and $\dim_\H( \mbox{Supp} T_l^+) \geq 2(k-l) + \frac{\log \chi_{2l}}{\psi_l}.$

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.

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

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

An idea expressed in the paper [Entropy 2017, 19, 345] about the deductive formulation of a physical theory resting on explicitly- and universally-introduced basic concepts is developed. An entropic measure of time with a number of properties leading to an analog of the Galilei–Einstein relativity principle is considered. Using the introduced measure and a simple model, a kinematic law relating the size, time, and number of particles of a system is obtained. Corollaries of this law are examined. In particular, accelerated increase of the system size and, if the system size remains unchanged, decrease of the number of particles are found. An interesting corollary is the emergence of repulsive and attractive forces inversely proportional to the square of the system size for relatively dense systems and constant for sufficiently rarefied systems.

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

The IoT Internet of Things being a promising technology of the future. It is expected to connect billions of devices. The increased communication number is expected to generate data mountain and the data security can be a threat. The devices in the architecture are fundamentally smaller in size and low powered. In general, classical encryption algorithms are computationally expensive and this due to their complexity and needs numerous rounds for encrypting, basically wasting the constrained energy of the gadgets. Less complex algorithm, though, may compromise the desired integrity. In this paper we apply a lightweight encryption algorithm named as Secure IoT (SIT) to a quantized speech image for Secure IoT. It is a 64-bit block cipher and requires 64-bit key to encrypt the data. This quantized speech image is constructed by first quantizing a speech signal and then splitting the quantized signal into frames. Then each of these frames is transposed for obtaining the different columns of this quantized speech image. Simulations result shows the algorithm provides substantial security in just five encryption rounds.

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

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

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

In the light of almost a century of struggle to make (common) sense of Quantum Mechanics and to reconcile it with General Relativity, it is proposed to (for some time) forget about quantizing gravity or striving for one Theory of Everything or “Weltformel”, which would describe the whole of reality without any joints or suture marks. Instead of one single monolithic formalism, a three-legged compound approach is argued for. Quantum Mechanics, Relativity and Thermodynamics are proposed as the main pillars of reality, each with its well-defined realm, specific features, and clearly marked interfaces between the three of them. Not only classical reality, which is rather directly accessible to us, is then comprehensively modelled by their encompassing combination. Quantum phenomena are understood as undoubtedly lying at the bottom of classical physics and at the same time, they become “fully real” only when embedded in classical frames between preparation and measurement in time. It is then where thermodynamics steps in and provides the mediating glue. The aim of this short contribution is not to deliver novel quantitative results but rather to propose a comprehensive research program and to coarsely lay out a very roughly coherent self-referential sketch starting from the beginning of the one universe, which we inhabit.

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.

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.

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.

Living systems must solve the problem of realizing their environment to act appropriately to maintain external relationships and internal order for survival and reproduction. This problem is a biological version of the philosophical enigma of how the self can escape solipsism. This study develops a comprehensive model to solve this adaptation problem. LSs must be composed of material entities that have the property of detecting their external states. The detection of the outside is conceptualized as “cognition,” a related state change that occurs at three levels of nested hierarchy: physical, chemical, and semiotic cognitions. Any entity that cognizes the surroundings is a “cognizer.” The hierarchical extension of cognition to all levels of the world provides a monistic view that only cognizers exist. Semiotic cognition is essential for the emergence and evolution of life. Living systems invented semiotic cognitions based on physical and chemical cognitions to manage the probability distribution of events that occur to them. This study proposes a theoretical model in which semiotic cognition is an adaptive process in which inverse causality operations produce particular internal states as symbols that signify hidden external states. This operation makes the living systems aware of the external world.

Coarse-grained molecular dynamics simulations are employed to investigate spatiotemporal evolution of vesicles (polymersomes) via self-assembly of randomly distributed amphiphilic diblock copolymers in water. Vesiculation pathway consists of several intermediate structures such as spherical/rodlike aggregates, wormlike micelles, lamellae, and cavities. Lamella to vesicle transition occurs at a constant aggregation number and is accompanied by a reduction in the solvent accessible surface area. Simulation predictions are in qualitative agreement with the mechanism of vesicle formation in which the unfavorable hydrophobic interactions between water molecules and polymer segments along the edge of the lamella are eliminated at the expense of gaining curvature energy. However, rod-lamella-vesicle transition is accompanied by an increase in copolymer packing density. Hence, the change in the surface area accompanying vesiculation predicted by the simulations is significantly lower than theoretical estimates. Changes in information entropy, quantified by the expectation of the logarithm of the probability distribution function of the segmental stretch parameter s, defined as the difference between the maximum and instantaneous segmental extension, are statistically insignificant along the vesiculation pathway. For rods, lamellae and polymersomes, s follows a log normal distribution. This is explained based on the configurational dynamics of a single diblock chain in water.

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

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

In this work, an entropy-stable and well-balanced numerical scheme for a one-dimensional blood flow model is presented. Such scheme is obtained from an explicit entropy conservative flux along with a second order discretization of the source term by using centered finite differences. We prove that the scheme is entropy-stable and preserves steady-states solutions. In addition, some numerical examples are included to test the performance of the proposed scheme.

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

Abstract: The high entropy alloy (HEA) of equiatomic composition CrNiFeCoMn and with FCC 11 crystal structure was prepared by either induction melting and additive manufacturing with a se- 12 lective laser melting (SLM) process, starting from mechanically alloyed powders. Unlike induction 13 melting, the as-produced SLM alloy showed fine nitride and Cr-rich s phase precipitates. Mechan- 14 ical spectroscopy measurements were performed on specimens cold worked and/or recrystallized. 15 Young’s modulus values of (140±10) GPa and (90±10) GPa were measured at 300 K for induction 16 melted and SLM samples, respectively. The values increased to (160±10) GPa and (170±10) GPa for 17 recrystallized samples. Damping measurements as a function of temperature showed two peaks 18 which were attributed to dislocations bending and grain boundaries sliding. The peaks were super- 19 posed on a temperature increasing background.

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

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

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

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

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

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

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

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

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

The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav-Weaire laws. The Voronoi entropy has been successfully applied to recently discovered self-assembled structures, such as patterned micro-porous polymer surfaces obtained by the breath figure method and levitating ordered water micro-droplet clusters.

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

Mexico is a well-known seismically active country, which is primarily affected by several tectonic plate interactions along the southern Pacific coastline and by active structures in the Gulf of Baja California. In this paper we investigate this seismicity in the context of a non-extensive statistical approach based on Tsallis entropy. The analysis is performed using data from the corrected Mexican seismic catalogue provided by the National Seismic Service, spanning a period from January 2000 to October 2023. The Gutenberg-Richter law fitting to the earthquake sub-catalogues for all six regions studied indicates magnitudes of completeness between 3.30 and 3.76. All six regions display values of the entropic index in the range 1.52≲q≲1.61, which are lower than the previously estimated range 1.54≲q≲1.70 using catalogue data from 1988 to 2010. The cause of this discrepancy is certainly due to the use of modern recording devices, which are sensitive enough to detect a larger number of low-magnitude events compared to older instrumentation.

We develop new theory from a broad case-study approach to explore a better understanding of what constitutes knowledge and its value as identifiable to human-machine teams. From past research, this trail of exploration will lead to these initial questions: What is the value of debate in the furtherance of knowledge? Will machines with AI be able to contribute to a debate if we humans cannot define it or determine its value sufficiently for a machine’s understanding, contribution, exploration and identification? Like humans, as teammates, machines must be able to determine with AI what constitutes the usable knowledge that contributes to a team’s success in the field (e.g., testing "knowledge" in the field, identifying new knowledge, using knowledge to develop innovation) or its failure (viz., trouble shooting; identifying weaknesses; discovering vulnerabilities, hiding by deception). It matters not whether a debate is public, private or unexpressed by an individual human or machine agent alone; we speculate in this exploration that the process advances the science of autonomous human-machine teams and assists in interpretable machine learning. We conclude with questions and a speculation: How does a human become aware or express its awareness of knowledge? Can a machine be as expressive as its human teammates? And how does a human-machine teammate become aware that its teammates possess sufficient knowledge to perform a task? We speculate that the structure of “knowledge," once found, is resistant to alternatives (i.e., it is ordered); that its functional utility is generalizable; and that its applications are multifaceted (akin to maximum entropy production). The complexity of the team is taken into consideration in our search for knowledge, which can also be used as an information metric.

Symmetry-breaking is a phenomenon that is observed in various contexts, from the early universe to complex organisms, and is considered a key puzzle in understanding the emergence of life. The presence of enantiomeric amino acids and proteins highlights its critical role. However, the origin of symmetry-breaking has yet to be comprehensively explained, particularly from an energetic standpoint. This article explores a novel approach by considering energy dissipation, specifically lost free energy, as a crucial factor in elucidating symmetry-breaking. Through a thorough thermodynamic analysis applicable to enantiomeric systems at various scales, from elementary particles to aggregated matter like crystals, we present experimental findings that establish a direct correlation between non-equilibrium free energy and energy dissipation during formation processes. Results emphasize the pivotal role of energy dissipation not only as an outcome but as the trigger for symmetry-breaking. This insight suggests that understanding the origins of complex systems, from cells to living beings and the universe itself, requires a lens focused on non-equilibrium processes, ultimately facilitating the formation of non-racemic systems.

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

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

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

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

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

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links are considered. Shannon-entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic β-colored convex polygons with m β-sides in the given complete graph. Introduced Shannon entropy is insensitive to the exact shape of the graph, but it is sensitive to the distribution of monochromatic polygons in a given graph. The introduced Shannon Entropies Sα and Sβ are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph, Sβ is, in turn, an average uncertainty to find the red β-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon Entropy is suggested. Various measures quantifying the Shannon Entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon Entropies are discussed.

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

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

Establishing an effective evaluation model to analyze the actual environmental level of the multi-indicator systems is an urgent challenge. However, due to the complexity of the environmental system, the factors that determine the practical system are usually interrelated. To solve this problem, many methods have been proposed and verified. However, the disadvantage of unreasonable weight determination and only single-indicator assessment limits the practical application of these analysis methods. Here, we established an optimized entropy weight model and integrate it with the fuzzy comprehensive evaluation (FCE) method to quantify the complex environmental system. By introducing the linear programming method into the entropy weight solution, we can obtain high accuracy weight values and strong resistance to extreme data. Theoretical and simulation results demonstrate that our method can enhance the precision of weight calculation and evaluation results for multi-factor systems. Our work develops an effective method to quantify the complex environment system comprehensively and is significant to real applications of evaluation method.

With the rapid development of the economy and the transformation of social contradictions, the economic development model in China has also changed, and a high-quality economic development model has been proposed. This paper uses the entropy method to measure the level of innovation and high-quality economic development in nine prefecture-level cities in Fujian Province from 2011 to 2020, and finds that the overall level shows an increasing trend year by year, but there are obvious regional differences. By constructing a grey correlation degree model, it is found that the innovation subsystem and the high-quality economic development are strongly correlated, the development level of innovation and the subsystem of high-quality economic development are both strongly correlated, the grey correlation degree from high to low is green, coordinated, shared, and livelihood, indicating that innovation has a significant impact on high-quality economic development. Based on the research results, countermeasures and suggestions are proposed to promote the coordinated development of innovation and high-quality economy.

The correlations of seismic noise, recorded during 1997-2022 at 229 stations around the world are investigated. The property of waveforms, known as the Donoho-Johnston threshold, is analyzed, which separates the absolute values of the orthogonal wavelet coefficients into "small" and "large". Network of 50 reference points is considered. For each reference point, a time series with a time step of 1 day is calculated as the median of the values of the DJ index from the 5 nearest stations. For each reference point, the correlations between the values of the DJ index at other reference points are calculated in a sliding time window of 365 days. Average values of the DJ index decrease, which is interpreted as indicators of global seismic hazard increasing. The maximum distances between reference points with strong correlations show an explosive increase after 2011. Bursts in the mean coherences between the length of day (LOD) and the values of the DJ index at the reference points precede the release of seismic energy with a delay of about 530 days. High amplitude of the DJ index response to LOD for the times 2020-2022 was identified, which may forecast a strong earthquake in the second half of 2023.

Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from a sells of equal size which are of a primary importance for decorative arts are reported. The pronounced prevalence of hexagons is inherent for the patterns with an equidistant and non-equidistant distribution of points, when the distance between the seed points is of the same order of magnitude as the distance between the turns of the spiral. Penta- and heptagonal “defected” cells appeared in the Voronoi diagrams due to the finite nature of the pattern. The ordered Voronoi tessellations demonstrating the Voronoi entropy larger than 1.71, reported for the random 2D distribution of points, were revealed. The dependence of the Voronoi entropy on the total number of the seed points located on the Archimedes Spirals is reported. Voronoi tessellations generated by the phyllotaxis-inspired patterns are addressed. The aesthetic attraction of the Voronoi mosaics arising from seed points placed on the Archimedes Spirals is discussed.

Spherically symmetric solution in 4D Einstein--Gauss--Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics (ModLogNED) is found. This solution at infinity possesses the charged black hole Reissner--Nordstr\"{o}m behavior. We study the black hole thermodynamics, entropy, shadow, energy emission rate and quasinormal modes. It was shown that black holes can possess the phase transitions and at some range of event horizon radii black holes are stable. The entropy has the logarithmic correction to the area law. The shadow radii were calculated for variety of parameters. We found that there is a peak of the black hole energy emission rate. The real and imaginary parts of the quasinormal modes frequencies were calculated. The energy conditions of ModLogNED are investigated.

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

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

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

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

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

This paper aims to provide an overall review of degradation, damage evolution and fatigue models in the literature of various engineering materials, mostly metals, and composites.

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

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

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

A precise understanding of the genes and associated genomes of SARS-CoV2 is important for various reasons such as discovering origin of the virus and virulence and so on. A thorough descriptive understanding of the SARS-CoV2 genomes and other coronavirus of the beta-coronavirus genus is primarily important. In this article, a set of ten genomes of four CoVs and their associated genes are considered for this present study. A spatial representations of nucleotide bases including purine-pyrimidine representations of the different genes of the corresponding genomes are quantified using Hurst exponent, Shannon entropy and density estimation of different nucleotides including GC content, in order to draw a comparison and contrast among the ten genomes of different types of CoVs which include MERS, SARS-CoV, HKU1 (Human Coronavirus) and associated their genes.

We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. The innovation that causal tensors introduce is that the framework allows for an exact expression of an indirect association in terms of the constituting, direct associations. This is not possible when expressing associations only in measures like mutual information or transfer entropy. Instead of a priori expressing associations in terms of mutual information or transfer entropy, the a posteriori expression of associations in these terms results in an intuitive definition of a nonnegative and left monotonic redundancy, which also meets the identity property. Our proposed redundancy satisfies the three axioms introduced by Williams and Beer. Symmetry and self-redundancy axioms follow directly from our definition. The data processing inequality ensures that the monotonicity axiom is satisfied. Because causal tensors can describe both mutual information as transfer entropy, the partial information decomposition applies to both measures. Results show that the decomposition closely resembles the decomposition of other another approach that expresses associations in terms of mutual information a posteriori. A negative synergistic term could indicate that there is an unobserved common cause.

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

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

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