搜索结果：Entropy (Basel, Switzerland)

The axiomatic structure of the κ-statistcal theory is proven. In addition to the first three standard Khinchin-Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the κ-entropy and its special limiting case, the classical Boltzmann-Gibbs-Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from κ-entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the κ-formalism, which emerges from the κ-entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on κ-entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the κ-statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized.

Some problems of describing biological systems with the use of entropy as a measure of the complexity of these systems are considered. Entropy is studied both for the organism as a whole and for its parts down to the molecular level. Correlation of actions of various parts of the whole organism, intercellular interactions and control, as well as cooperativity on the microlevel lead to a more complex structure and lower statistical entropy. For a multicellular organism, entropy is much lower than entropy for the same mass of a colony of unicellular organisms. Cooperativity always reduces the entropy of the system; a simple example of ligand binding to a macromolecule carrying two reaction centers shows how entropy is consistent with the ambiguity of the result in the Bernoulli test scheme. Particular attention is paid to the qualitative and quantitative relationship between the entropy of the system and the cooperativity of ligand binding to macromolecules. A kinetic model of metabolism. corresponding to Schrödinger's concept of the maintenance biosystems by "negentropy feeding", is proposed. This model allows calculating the nonequilibrium local entropy and comparing it with the local equilibrium entropy inherent in non-living matter.

BACKGROUND: As the world's largest coal producer, China was accounted for about 46% of global coal production. Among present coal mining risks, methane gas (called gas in this paper) explosion or ignition in an underground mine remains ever-present. Although many techniques have been used, gas accidents associated with the complex elements of underground gassy mines need more robust monitoring or warning systems to identify risks. This paper aimed to determine which single method between the PCA and Entropy methods better establishes a responsive weighted indexing measurement to improve coal mining safety. METHODS: Qualitative and quantitative mixed research methodologies were adopted for this research, including analysis of two case studies, correlation analysis, and comparative analysis. The literature reviewed the most-used multi-criteria decision making (MCDM) methods, including subjective methods and objective methods. The advantages and disadvantages of each MCDM method were briefly discussed. One more round literature review was conducted to search publications between 2017 and 2019 in CNKI. Followed two case studies, correlation analysis and comparative analysis were then conducted. Research ethics was approved by the Shanxi Coking Coal Group Research Committee. RESULTS: The literature searched a total of 25,831publications and found that the PCA method was the predominant method adopted, and the Entropy method was the second most widely adopted method. Two weighting methods were compared using two case studies. For the comparative analysis of Case Study 1, the PCA method appeared to be more responsive than the Entropy. For Case Study 2, the Entropy method is more responsive than the PCA. As a result, both methods were adopted for different cases in the case study mine and finally deployed for user acceptance testing on 5 November 2020. CONCLUSIONS: The findings and suggestions were provided as further scopes for further research. This research indicated that no single method could be adopted as the better option for establishing indexing measurement in all cases. The practical implication suggests that comparative analysis should always be conducted on each case and determine the appropriate weighting method to the relevant case. This research recommended that the PCA method was a dimension reduction technique that could be handy for identifying the critical variables or factors and effectively used in hazard, risk, and emergency assessment. The PCA method might also be well-applied for developing predicting and forecasting systems as it was sensitive to outliers. The Entropy method might be suitable for all the cases requiring the MCDM. There is also a need to conduct further research to probe the causal reasons why the PCA and Entropy methods were applied to each case and not the other way round. This research found that the Entropy method provides higher accuracy than the PCA method. This research also found that the Entropy method demonstrated to assess the weights of the higher dimension dataset was higher sensitivity than the lower dimensions. Finally, the comprehensive analysis indicates a need to explore a more responsive method for establishing a weighted indexing measurement for warning applications in hazard, risk, and emergency assessments.

Nonalcoholic fatty liver disease (NAFLD) is the leading cause of advanced liver diseases. Fat accumulation in the liver changes the hepatic microstructure and the corresponding statistics of ultrasound backscattered signals. Acoustic structure quantification (ASQ) is a typical model-based method for analyzing backscattered statistics. Shannon entropy, initially proposed in information theory, has been demonstrated as a more flexible solution for imaging and describing backscattered statistics without considering data distribution. NAFLD is a hepatic manifestation of metabolic syndrome (MetS). Therefore, we investigated the association between ultrasound entropy imaging of NAFLD and MetS for comparison with that obtained from ASQ. A total of 394 participants were recruited to undergo physical examinations and blood tests to diagnose MetS. Then, abdominal ultrasound screening of the liver was performed to calculate the ultrasonographic fatty liver indicator (US-FLI) as a measure of NAFLD severity. The ASQ analysis and ultrasound entropy parametric imaging were further constructed using the raw image data to calculate the focal disturbance (FD) ratio and entropy value, respectively. Tertiles were used to split the data of the FD ratio and entropy into three groups for statistical analysis. The correlation coefficient r, probability value p, and odds ratio (OR) were calculated. With an increase in the US-FLI, the entropy value increased (r = 0.713; p < 0.0001) and the FD ratio decreased (r = –0.630; p < 0.0001). In addition, the entropy value and FD ratio correlated with metabolic indices (p < 0.0001). After adjustment for confounding factors, entropy imaging (OR = 7.91, 95% confidence interval (CI): 0.96–65.18 for the second tertile; OR = 20.47, 95% CI: 2.48–168.67 for the third tertile; p = 0.0021) still provided a more significant link to the risk of MetS than did the FD ratio obtained from ASQ (OR = 0.55, 95% CI: 0.27–1.14 for the second tertile; OR = 0.42, 95% CI: 0.15–1.17 for the third tertile; p = 0.13). Thus, ultrasound entropy imaging can provide information on hepatic steatosis. In particular, ultrasound entropy imaging can describe the risk of MetS for individuals with NAFLD and is superior to the conventional ASQ technique.

The lightweight and flexible materials can improve people’s quality of daily life; in addition, the materials can be widely used in aerospace, automotive, consumer electronics, etc. Recently, high-entropy alloys had become hot issues in materials science with many excellent properties; therefore, we can combine the design ideas of high-entropy alloys with lightweight materials and flexible materials, taking into account the advantages of two types of materials, and promoting the development and progress of new materials. In the chapter, we will elaborate on the relationship between the microstructure and properties of lightweight high-entropy alloys and the design ideas of high-entropy alloys with flexible materials that were investigated in recent years. Furthermore, as the microstructure and mechanical properties of the alloys exhibit the nonlinear behaviors with entropy on high-entropy alloys, we would like to define the lightweight high-entropy alloy as the density is lower than 6 g/cm3, the mix-entropy of these alloys is higher than 1R (here, R is gas constant), and the number of components is four or more. Finally, it is expected to broaden the research field of high-entropy alloys and provide some new directions for the development of new materials.

High-entropy materials (HEMs) constitute a revolutionary class of materials that have garnered significant attention in the field of materials science, exhibiting extraordinary properties in the realm of energy storage. These equimolar multielemental compounds have demonstrated increased charge capacities, enhanced ionic conductivities, and a prolonged cycle life, attributed to their structural stability. In the anode, transitioning from the traditional graphite (372 mAh g−1) to an HEM anode can increase capacity and enhance cycling stability. For cathodes, lithium iron phosphate (LFP) and nickel manganese cobalt (NMC) can be replaced with new cathodes made from HEMs, leading to greater energy storage. HEMs play a significant role in electrolytes, where they can be utilized as solid electrolytes, such as in ceramics and polymers, or as new high-entropy liquid electrolytes, resulting in longer cycling life, higher ionic conductivities, and stability over wide temperature ranges. The incorporation of HEMs in metal–air batteries offers methods to mitigate the formation of unwanted byproducts, such as Zn(OH)4 and Li2CO3, when used with atmospheric air, resulting in improved cycling life and electrochemical stability. This review examines the basic characteristics of HEMs, with a focus on the various applications of HEMs for use as different components in lithium-ion batteries. The electrochemical performance of these materials is examined, highlighting improvements such as specific capacity, stability, and a longer cycle life. The utilization of HEMs in new anodes, cathodes, separators, and electrolytes offers a promising path towards future energy storage solutions with higher energy densities, improved safety, and a longer cycling life.

Fault diagnosis of rotating machinery is vital to identify incipient failures and avoid unexpected downtime in industrial systems. This paper proposes a new rolling bearing fault diagnosis method by integrating the fine-to-coarse multiscale permutation entropy (F2CMPE), Laplacian score (LS) and support vector machine (SVM). A novel entropy measure, named F2CMPE, was proposed by calculating permutation entropy via multiple-scale fine-grained and coarse-grained signals based on the wavelet packet decomposition. The entropy measure estimates the complexity of time series from both low- and high-frequency components. Moreover, the F2CMPE mitigates the drawback of producing time series with sharply reduced data length via the coarse-grained procedure in the conventional composite multiscale permutation entropy (CMPE). The comparative performance of the F2CMPE and CMPE is investigated by analyzing the synthetic and experimental signals for entropy-based feature extraction. In the proposed bearing fault diagnosis method, the F2CMPE is first used to extract the entropy-based features from bearing vibration signals. Then, LS and SVM are used for selection of features and fault classification, respectively. Finally, the effectiveness of the proposed method is verified for rolling bearing fault diagnosis using experimental vibration data sets, and the results have demonstrated the capability of the proposed method to recognize and identify the bearing fault patterns under different fault states and severity levels.

We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schr\"odinger field theory at finite density and zero temperature, which is a non-relativistic model with Lifshitz exponent $z=2$. We prove that the entanglement entropies are finite functions of one dimensionless parameter proportional to the area of a rectangular region in the phase space determined by the Fermi momentum and the length of the interval. The entanglement entropy is a monotonically increasing function. By employing the properties of the prolate spheroidal wave functions of order zero or the asymptotic expansions of the tau function of the sine kernel, we find analytic expressions for the expansions of the entanglement entropies in the asymptotic regimes of small and large area of the rectangular region in the phase space. These expansions lead to prove that the analogue of the relativistic entropic $C$ function is not monotonous. Extending our analyses to a class of free fermionic Lifshitz models labelled by their integer dynamical exponent $z$, we find that the parity of this exponent determines the properties of the bipartite entanglement for an interval on the line.

Abstract The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics. Furthermore, it has provided a natural framework to study basins of attraction in nonlinear dynamics and new criteria for the detection of fractal boundaries. In this article, we describe the concept as well as fundamental applications. In addition, we provide our perspective on the future challenges of applying the basin entropy idea to understanding complex systems.

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

The existence of noise has great influence on the real features of observed time series, thus noise reduction in time series data is a necessary and significant task in many practical applications. When using traditional de-noising methods, the results often cannot meet the practical needs due to their inherent shortcomings. In the present paper, first a set of key but difficult wavelet de-noising problems are discussed, and then by applying information entropy theories to the wavelet de-noising process, i.e., using the principle of maximum entropy (POME) to describe the random character of the noise and using wavelet energy entropy to describe the degrees of complexity of the main series in original series data, a new entropy-based wavelet de-noising method is proposed. Analysis results of both several different synthetic series and typical observed time series data have verified the performance of the new method. A comprehensive discussion of the results indicates that compared with traditional wavelet de-noising methods, the new proposed method is more effective and universal. Furthermore, because it uses information entropy theories to describe the obviously different characteristics of noises and the main series in the series data is observed first and then de-noised, the analysis process has a more reliable physical basis, and the results of the new proposed method are more reasonable and are the global optimum. Besides, the analysis process of the new proposed method is simple and is easy to implement, so it would be more applicable and useful in applied sciences and practical engineering works.

Microwaves at the ISM (Industrial, Scientific and Medical, reserved internationally) frequency of 2450 or 5800 MHz have been used to prepare FeCoNiCuAl, FeCrNiTiAl and FeCoCrNiAl2.5 high entropy alloys by direct heating of pressed mixtures of metal powders. The aim of this work is to explore a new microwave-assisted near-net-shape technology, using a powder metallurgy approach for the preparation of high entropy alloys, able to overcome the limits of current melting technologies (defects formation) or solid state ones (time demanding). High entropy alloy compositions have been selected so as to comprise at least one ferromagnetic element and one highly reactive couple, like Ni-Al, Ti-Al, Co-Al or Fe-Al. Results show that direct microwave heating of the powder precursors occurs, and further heating generation is favored by the ignition of exothermal reactions in the load. Microwaves have been applied both for the ignition and sustaining of such reactions, showing that by the proposed technique, it is possible to control the cooling rate of the newly-synthesized high entropy alloys. Results showed also that microwave heating in predominant magnetic field regions of the microwave applicator is more effective at controlling the cooling rate. The herein proposed microwave-assisted powder metallurgy approach is suitable to retain the shape of the load imparted during forming by uniaxial pressing. The homogeneity of the prepared high entropy alloys in all cases was good, without the dendritic segregation typical of arc melting, even if some partially-unreacted powders were detected in the samples.

In this paper we propose a methodology to study circular economy processes based on mathematical modelling. In open-ended systems, waste could be converted back to recycling, transforming the economy from linear to circular. The concept of entropy and the second law of thermodynamics give the argument for a scale reduction of material circulation. As humans extract more and more energy and matter for the economy, the degree of entropy is likely to increase. Based on the findings of economic studies on the implications of industrialization in the case of growing economies, this study aims at evaluating circular economy processes at the European Union (EU) level using a Shannon-Entropy-based algorithm. An entropy-based analysis was conducted for the 28 European Union countries during the time frame 2007–2016. The modelling process consists of constructing a composite indicator which is composed of a weighted sum of all indicators developed by an algorithm based on Shannon Entropy. The weights assigned to each indicator in our analysis measure the significance of each indicator involved in the development of the composite indicator. The results are similar to the international rakings, consolidating and confirming the accuracy and reliability of this approach.

Although there have been extensive studies on CoCrFeNi high entropy alloys (HEAs), they are still far from industrial applications due to their inferior strength. Based on the approach of interstitial atom strengthening which has been shown to be one of the effective ways to modify the properties of metallic materials, a series of (CoCrFeNi)100-xNx (x = 0, 0.25 and 0.50 at. %) HEAs were prepared in this study by selective laser melting (SLM). It was found that nitrogen addition in CoCrFeNi HEA can slightly refine the microstructure but did not change the preferred orientations after SLM. By increasing the nitrogen content in the matrix, the strength increases while the ductility is reduced. Also, the addition of nitrogen in CoCrFeNi HEA can decrease the stacking fault probability, leading to the increased stacking fault energy (SFE) in N-doped CoCrFeNi HEA. The increased strength in N-doped CoCrFeNi HEA samples mainly attributes to the solid solution strengthening of nitrogen, whereas the ductility loss results from the impediment on the formation of deformed twins induced by increased SFE. These results can provide a new strategy for designing high-strength N-doped HEAs.

We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with d levels each. It can be described by the Rényi–Ingarden–Urbanik entropy Sq of a decomposition of the state in a product basis, minimized over all local unitary transformations. In the case q = 0, this quantity becomes a function of the rank of the tensor representing the state, while in the limit q → ∞, the entropy becomes related to the overlap with the closest separable state and the geometric measure of entanglement. For any bipartite system, the entropy S1 coincides with the standard entanglement entropy. We analyze the distribution of the minimal entropy for random states of three- and four-qubit systems. In the former case, the distribution of the three-tangle is studied and some of its moments are evaluated, while in the latter case, we analyze the distribution of the hyperdeterminant. The behavior of the maximum overlap of a three-qudit system with the closest separable state is also investigated in the asymptotic limit.

High entropy or multi principal element alloys are a promising and relatively young concept for designing alloys. The idea of creating alloys without a single main alloying element opens up a wide space for possible new alloy compositions. High entropy alloys based on refractory metals such as W, Mo, Ta or Nb are of interest for future high temperature applications e.g., in the aerospace or chemical industry. However, producing refractory metal high entropy alloys by conventional metallurgical methods remains challenging. For this reason, the feasibility of laser-based additive manufacturing of the refractory metal high entropy alloy W20Mo20Ta20Nb20V20 by laser powder bed fusion (PBF-LB/M) is investigated in the present work. In-situ alloy formation from mixtures of easily available elemental powders is employed to avoid an expensive atomization of pre-alloyed powder. It is shown that PBF-LB/M of W20Mo20Ta20Nb20V20 is in general possible and that a complete fusion of the powder mixture without a significant number of undissolved particles is achievable by in-situ alloy formation during PBF-LB/M when selecting favorable process parameter combinations. The relative density of the samples with a dimension of 6 × 6 × 6 mm3 reaches, in dependence of the PBF-LB/M parameter set, 99.8%. Electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) measurements confirm the presence of a single bcc-phase. Scanning electron microscopy (SEM) images show a dendritic and/or cellular microstructure that can, to some extent, be controlled by the PBF-LB/M parameters.

The second law of thermodynamics, with its positive change of entropy for a system not in equilibrium, defines an arrow of time. Interestingly, also, causality, which is the connection between a cause and an effect, requests a direction of time by definition. It is noted that no other standard physical theories show this property. It is the attempt of this work to connect causality with entropy, which is possible by defining time as the metric of causality. Under this consideration that time appears only through a cause-effect relationship ("measured", typically, in an apparatus called clock), it is demonstrated that time must be discrete in nature and cannot be continuous as assumed in all standard theories of physics including general and special relativity, and classical physics. The following lines of reasoning include: (i) (mechanical) causality requests that the cause must precede its effect (i.e., antecedence) requesting a discrete time interval >0. (ii) An infinitely small time step d t > 0 is thereby not sufficient to distinguish between cause and effect as a mathematical relationship between the two (i.e., Poisson bracket) will commute at a time interval d t , while not evidently within discrete time steps Δ t . As a consequence of a discrete time, entropy emerges (Riek, 2014) connecting causality and entropy to each other.

The classical Lighthill-Whitham-Richards (LWR) kinematic traffic model is extendedto a unidirectional road on which the maximum density $a(x)$represents roadinhomogeneities, such as variable numbers of lanes, and is allowedto vary discontinuously. The car density$\phi = \phi(x,t)$ is then determined by the followinginitial value problem fora scalar conservation law with a spatially discontinuous flux: $\phi_t + (\phi v(\phi/{a(x)})_x = 0, \quad \phi(x,0)=\phi_0(x),\quad x \in \mathbb{R},\quad t\in (0,T),$ (*)where $v(z)$ is the velocity function. We adapt to (*) a new notionof entropy solutions (Bürger, Karlsen, and Towers[Submitted, 2007]), which involves a Kružkov-typeentropy inequality based on a specific flux connection $(A,B)$, and which we interpret in terms of traffic flow. This conceptis consistent with both the driver's ride impulseand the desire ofdrivers to speed up. We prove that entropy solutionsof type $(A,B)$ are unique. This solution concept also leads to simple, transparent, and unified convergence proofs fornumerical schemes. Indeed, we adjust to (*) new variants of the Engquist-Osher (EO) scheme(Bürger, Karlsen, and Towers [Submitted, 2007]),and of the Hilliges-Weidlich (HW) scheme analyzedby the authors [ J. Engrg. Math., to appear].It is proven that the EO and HW schemes and a related Godunov schemeconverge to the unique entropy solution of type $(A,B)$ of (*). For the Godunov version, this is the first rigorous convergence and well-posedness result, since nounnecessarily restrictive regularity assumptions are imposed on the solution.Numerical experiments for first-order schemes andformally second-orderMUSCL/Runge-Kutta versions are presented.

High-entropy alloys can either be defined as solid solution alloys containing at least five elements in equiatomic or near-equiatomic composition, or as alloys with high configurational entropies (larger than 1.5R), regardless of the number of elements involved. The present study reports on an alloy design route for refractory high-entropy alloys based on equiatomic Mo-Nb-V alloys with additions of W and Ti. In general, the work was motivated by Senkov et al. The aim of the experiments carried out was to produce a refractory high-entropy alloy with a single-phase structure. For this purpose, a systematic alloy design involving four- and five-element compositions was used. Scanning electron microscopy analysis has shown that Mo-Nb-V-xW-yTi (x = 0, 20; y = 5, 10, 15, 20, 25) is in fact a refractory high-entropy alloy with a body-centered cubic dendritic structure. Furthermore, the Ti-concentration of the experimental alloys was varied, to obtain the influence of Titanium on the microstructure development. Additionally, compressive tests at room temperature were carried out to evaluate the influence of the different alloying elements and the Ti-fraction on the mechanical properties. The observations of the present work are then compared to the published results on similar alloys from the working group of Yao et al. and critically discussed.