Classical Entropy Research Articles

Classical entanglement and entropy

Motivated by recent discussions of entanglement in the context of high energy scattering, we consider the relation between the entanglement entropy of a highly excited state of a quantum system and the classical entanglement entropy of the corresponding classical system. We show on the example of two weakly coupled harmonic oscillators that the two entropies are equal. Quantum mechanically, the reduced density matrix which yields this entropy is close to the maximally entangled state. We thus observe that the nature of entanglement in this type of state is purely classical.

Real-time EEG-based detection of driving fatigue using a novel semi-dry electrode with self-replenishment of conductive fluid

A novel semi-dry electrode that can realize self-replenishment of conductive liquid is proposed in this study. Driving fatigue is detected by extracting the refined composite multiscale fluctuation dispersion entropy (RCMFDE) features in electroencephalogram (EEG) signals collected by this electrode. The results show that the new semi-dry electrode can automatically complete the conductive fluid supplement according to its own humidity conditions, which not only notably improves the effective working time, but also significantly reduces the skin impedance. By comparing with the classical entropy algorithms, the computational speed and the stability of the RCMFDE method are Substantially enhanced.

Optimization by linear kinetic equations and mean-field Langevin dynamics

One of the most striking examples of the close connections between global optimization processes and statistical physics is the simulated annealing method, inspired by the famous Monte Carlo algorithm devised by Metropolis et al. in the middle of last century. In this paper, we show how the tools of linear kinetic theory allow the description of this gradient-free algorithm from the perspective of statistical physics and how convergence to the global minimum can be related to classical entropy inequalities. This analysis highlights the strong link between linear Boltzmann equations and stochastic optimization methods governed by Markov processes. Thanks to this formalism, we can establish the connections between the simulated annealing process and the corresponding mean-field Langevin dynamics characterized by a stochastic gradient descent approach. Generalizations to other selection strategies in simulated annealing that avoid the acceptance–rejection dynamic are also provided.

Topological entropy of i.i.d. case and free semigroup actions

In this paper, firstly we give a new condition to prove that classical topological entropy is equal to Pesin topological entropy in i.i.d. case. After that, we generalize the concepts of topological entropy of free semigroup actions and study the relationship between the entropies of i.i.d. case and the entropies of free semigroup actions. Finally, for any non-empty subset A⊆Σm+, we introduce the concepts of entropies of any subset A actions and give an analogue of Befutov's formula (the Theorem 1 in [6]) under any subset A actions, which is a supplement of [7].

Entropic Advancement To Education

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

Classical information entropy of parton distribution functions and an application in searching gluon saturation

Classical information entropy of parton distribution functions and an application in searching gluon saturation

Cosmological FLRW phase transitions and micro-structure under Kaniadakis statistics

This article studies the thermodynamics phase transitions and critical phenomena of an FLRW cosmological model under truncated Kaniadakis's statistics. The EoS is derived from the corrected Friedmann field equations and the thermodynamics unified first law. To approach thermodynamics, we use an approximation for KSAH≪1, on the cosmological equation, and also check the validity of our approximation. Then for different values from Kaniadakis parameter K, order O(10−37) for the relic-abundance, O(10−84) for 7Li-abundance and O(10−125) in the recombination era, the EoS reveals non-trivial critical points where a first-order phase transition occurs a sort of a van der Waals fluid. Interestingly, the numerical values of the critical exponents are the same as those of the van der Waals system. Besides, to obtain more insights into the thermodynamics description, the so-called Ruppeiner's geometry is studied through the normalized scalar curvature, disclosing this invariant zone where the system undergoes repulsive/attractive interactions. Near the critical point, this curvature provides again the same critical exponent and universal constant value as for van der Waals fluid. Despite the similarity, both systems are quite different because the present one considers a relativistic entropy (Kaniadakis entropy) while the Van der Waals gas responds to a classical entropy (Maxwell-Boltzmann).

An entropy‐based model for quantifying multi‐dimensional traffic scenario complexity

AbstractQuantifying the complexity of traffic scenarios not only provides an essential foundation for constructing the scenarios used in autonomous vehicle training and testing, but also enhances the robustness of the resulting driving decisions and planning operations. However, currently available quantification methods suffer from inaccuracies and coarse‐granularity in complexity measurements due to issues such as insufficient specificity or indirect quantification. The present work addresses these challenges by proposing a comprehensive entropy‐based model for quantifying traffic scenario complexity across multiple dimensions based on a consideration of the essential components of the traffic environment, including traffic participants, static elements, and dynamic elements. In addition, the limitations of the classical information entropy models applied for assessing traffic scenarios are addressed by calculating magnitude entropy. The proposed entropy‐based model is analyzed in detail according to its application to simulated traffic scenarios. Moreover, the model is applied to real world data within a naturalistic driving dataset. Finally, the effectiveness of the proposed quantification model is illustrated by comparing the complexity results obtained for three typical traffic scenarios with those obtained using an existing multi‐factor complexity quantification method.

Mechanical-thermal coupling fatigue failure of CoCrFeMnNi high entropy alloy

High entropy alloys exhibit excellent performance under different-temperature conditions. In order to investigate the effect of temperature on the mechanical-thermal coupling fatigue failure of classical CoCrFeMnNi high entropy alloy to accelerate the application of high entropy alloys, the uniaxial tensile and fatigue tests at temperatures ranging from RT to 500 °C were conducted, and statics simulation analysis of fatigue specimens under fatigue loading conditions was conducted. The results of the uniaxial tensile tests illustrated that the yield stress and tensile strength of the alloy decreased with increasing temperature. In contrast, the elongation after the fracture of the alloy increased with temperature. The fatigue test results revealed that the fatigue life decreased as the temperature increased. The fracture morphology of the fatigue specimens and the flank morphology and dislocation distribution near the crack nucleation zone were collected to support the investigation. Accordingly, the reasons for the high-temperature-induced decrease in fatigue crack nucleation and propagation lives were systematically investigated. The main reasons for the higher-temperature-induced decrease in crack nucleation lives were a decrease in the yield stress of the alloy, more easily triggered dislocation motion and stress homogenization. The reasons for the decrease in fatigue crack propagation lives induced by higher temperatures were the more prone occurrence of dislocation motion, a decrease in yield stress, and a decrease in the area of the crack propagation region.

A variation on von Neumann Entropy and a result of Varadarajan

Thirty years ago, I had just completed my Ph.D. under Varadarajan when, as part of a subsequent reading course, he and I considered a generalization of von Neumann entropy, here called a matrix entropy, computed by using the classical entropy function on the diagonals of density matrices. I had asked whether the value of von Neumann entropy was the maximum of the matrix entropy on a given unitary equivalence class. Varadarajan soon sketched a proof of this, which is presented here. It serves as a nice way to see classical entropy sitting in the von Neumann entropy context, and a reminder for this short note’s author of a pleasant time spent working with a remarkable scholar and teacher.

Fractal perspective on dynamics of dark matter and dark energy interactions

In this paper, the dynamics of intricate chaotic attractors of the nonlinear system modeling the dark matter and dark energy interactions is studied indulging fractal–fractional operator in the Caputo sense. The constructed strange attractors witness that the dynamics of the universe components is dominated by the fractal properties. The fractional entropies stemmed from the classical entropy are estimated with fractal parameter and graphically portrayed to measure the randomness of the dynamic variables associated with the proposed dynamical system.

New distance measure-driven flexible linguistic consensus model with application to urban flooding risk assessment

As a novel linguistic representation tool, flexible linguistic expression (FLE) has substantial flexibility in expressing ambiguous and uncertain information from experts. However, FLEs pose the following challenges to developing information measurement and consensus mechanisms for FLEs-based multi-attribute group decision-making (MAGDM). (1) The current studies primarily use linguistic distribution approximation or triangular fuzzy numbers to measure the difference between FLEs indirectly without proposing an exact distance measure. (2) Few studies have been conducted on direct accurate consensus models incorporating adaptive consensus feedback mechanisms. To deal with these issues, the flexible linguistic ordinal Deng entropy (FLODE) is firstly proposed to measure the uncertainty of FLEs, and by combining it with linguistic scale functions, a new distance measure for FLEs is constructed, which can accurately measure the level of group consensus and the difference in pairwise FLEs. Subsequently, by integrating the defined FLODE with the classical entropy weight method, a new method for determining the experts’ personalized attribute weights is constructed, fully considering the impact of experts’ personalized attribute weights on decision-making results. Also, a new consensus model incorporating a minimum adjustment feedback mechanism and dynamic personalized attribute weights is developed, in which the feedback adjustment coefficients and personalized attribute weights are dynamically updated during the consensus reaching process (CRP). Lastly, an urban flooding risk assessment is applied to confirm the effectiveness of the proposed consensus model.

Quantum Entropy and the Mechanism of Gravity

Quantum entropy measures the number of possible microstates of position and momentum due to quantum uncertainty. Black hole entropy is an example of quantum entropy. Classical entropy, like the Gibbs entropy of a gas, does not depend on quantum uncertainty. This paper is the first to define the quantum entropy of ordinary matter, termed “atomic entropy”. The atomic entropy at the surface of a spherical object depends on its mass and is inversely proportional to its surface area. The entropy scale factor (ESF) is a theory that all changes in the scale of spacetime are due to differences in entropy. Defining atomic entropy allows the ESF to make predictions for systems including ordinary matter. In the ESF, gravitational objects are attracted to one another because gravitational entropy, a form of quantum entropy, increases as the distance between these objects decreases. The increase in gravitational entropy increases the total entropy of the system, in accordance with the second law of thermodynamics. This paper is also the first to use the gradients in the scale of space and time predicted by the ESF to derive Newtonian gravity. Explaining the mechanism of gravity in this way provides a link between quantum physics and gravity.

Quantum to classical parton evolution in the QGP

We study the time evolution of the density matrix of a high energy quark in the presence of a dense QCD background that is modeled as a stochastic Gaussian color field. At late times, we find that only the color singlet component of the quark’s reduced density matrix survives the in-medium evolution and that the density matrix becomes asymptotically diagonal in both transverse position and momentum spaces. In addition, we observe an accelerated entropy growth due to the larger phase space being explored by the quark and that the quantum and classical quark entropies converge at late times. We further observe that the quark state loses all memory of the initial condition. Combined with the fact that the reduced density matrix satisfies Boltzmann-diffusion transport, we conclude that the quark reduced density matrix can be interpreted as a classical phase space distribution.

THE FRACTIONAL DISEN–FISHER PLANE: AN EFFECTIVE APPROACH TO DISTINGUISH COMPLEX TIME SERIES

With the explosive growth of data quantity and rapid development of nonlinear dynamics as well as the growing demand for complex data classification in the field of artificial intelligence and machine learning, the research of complex time series, generated by complex systems, has attracted enormous interests. However, how to simultaneously distinguish different types of time series data and extract more accurate and detailed information from them in the light of localized and global scale perspectives remains significant and needs to be tackled. Thus, in this paper, we propose the fractional DisEn–Fisher plane, which is innovatively constructed by the fractional form of dispersion entropy and Fisher information measure. These are both effective tools to diagnose the essential properties of complex time series, to analyze the complexity of systems and to depict the contained statistical information with higher accuracy and effectiveness. Several classical entropy plane methods are selected as a comparison to design simulation experiments by simulated data and three real-world datasets. Comparative experimental results show that this method is a feasible and reliable improvement method, which will help to provide more additional information in time series recognition and dynamic characterization. It may not only provide new insights for further improvement of complex time series analysis, but also have important implications for developing complex data clustering methods.

On the Use of a Complex Indicator of the Stability of Permutation Entropy of Time Series Fragments When Analyzing Infrasound Monitoring Signals of the Altai Republic

This paper discusses one of the approaches that allows us to assess the degree of complexity or randomness of fragments of a time series in order to detect infrasound or geomagnetic signals in the results of observations of the dynamics of the natural or man-made processes under study. In our case, we are talking about monitoring the infrasound background on the territory of the Altai Republic. To solve the problem of estimating the required characteristics of a time series with minimal computational costs and in real time, a complex indicator of the stability of permutation entropy is introduced, since estimating the value of classical permutation entropy for n = 3 (the most commonly used version of permutation entropy) does not allow solving the problem with sufficient accuracy.

Fast Estimation of Entropy Profiles for Lithium-Ion Batteries

The operating temperature of a lithium-ion battery (LIB) has strong effects on its electrochemical performance, safety, and lifetime. Reliable predictions of cell temperature and heat generation are required for the design and thermal management of battery systems. During the normal operation of LIBs, heat sources can be classified into irreversible heat from resistive losses such as ohmic resistance, charge-transfer overpotentials, and mass-transfer limitations; and reversible heat from entropy change . The irreversible heat generation is related to the cell's internal resistance and the applied current. The reversible heat depends on the entropy variation of electrode materials, the state of charge (SoC), and the temperature. An accurate measurement of entropy-variation will not only help to improve the battery operation under optimal thermal conditions but can also be used to diagnose the battery aging since it can reveal crystal structure changes in the electrodes [1, 2].Techniques for measuring the entropy of a battery can mainly be classified into potentiometric [3] and calorimetric methods. The potentiometric method measures the open circuit voltage (OCV) changes while the cell temperature is varied at different SoCs. This method requires a long relaxation time to obtain the OCV equilibrium state following each SoC point and temperature step. The calorimetric method [4-6] is based on measuring the heat generation during charge and discharge, and various models are applied to differentiate between and quantify the reversible and irreversible heat sources. The entropy variation with SOC is obtained via the reversible heat rate.Recent improved methods include e.g., Schmidt et al. [4] who proposed a reversible heat extraction method based on electrothermal impedance spectroscopy (ETIS) and Damay et al. [5] proposing a fast calorimetric method to obtain a continuous entropy profile. The cell surface temperature is monitored while the battery is charged and discharged continuously. A thermal balance is used to estimate the heat generation from the monitored cell temperature changes during charge and discharge. The benefit of this method can be low cost, fast and high resolution. Bedürftig et al. [6] proposed a calorimetric method named ‘Double Pulse Method’ to measure reversible heat in lithium-ion battery cells by exciting the cell with charge and discharge current pulses.Here we present a new entropy characterization method via charge and discharge cycles of a LIB at low constant C-rates using simple insulating condition. Through monitoring the variations of cell surface temperature and voltage with the state of charge, the continuous variation of entropy with the state of charge can be extracted. These results were compared to classical entropy measurements obtained through the potentiometric method as shown in Figure 1. In addition, the extracted entropy variation data is input into a LIB modelling approach, combining a P2D-electrochemical sub-model for battery operation and a 3D-finite-element sub-model for thermal behavior while battery charge and discharge. The model predictions on the cell outer surface temperature variation while charge and discharge under different C-rates are compared with the data obtained in the battery characterization tests as shown in Figure 2. Good agreements between the model predictions and tests are achieved.

Cumulative information generating function and generalized Gini functions

We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival function. Specifically, after establishing its main properties and some bounds, we show that it is a variability measure itself that extends the Gini mean semi-difference. We also provide (i) an extension of such a measure, based on distortion functions, and (ii) a weighted version based on a mixture distribution. Furthermore, we explore some connections with the reliability of k-out-of-n systems and with stress–strength models for multi-component systems. Also, we address the problem of extending the cumulative information generating function to higher dimensions.

Why Thermodynamic Entropy and Statistical Entropy are Two Different Physical Quantities

Background: Historically, the coincidence of classical thermodynamic entropy and statistical entropy is based on an assumption (the so-called Boltzmann-Planck relation). The study shows that the Boltzmann-Planck relation is not valid in general. Aims: The study demonstrates that thermodynamic entropy is a physical entity distinct from statistical entropy. Methods: Initially, the entropy of ideal gases is examined and demonstrated to be independent of the gas volume. The ideal gas's true entropy is then expressed correctly. Results: The Boltzmann-Planck entropy equation is demonstrated to be incapable of describing the thermodynamic entropy of ideal gases. Conclusion: In general, the Boltzmann-Planck entropy cannot be considered a statistical interpretation of the thermodynamic entropy. The two entropies represent two different physical quantities. The physical quantity that enters the second law of thermodynamics is the thermodynamic entropy, not the statistical entropy. 6: The study advocates for a fundamental rethinking of today's statistical understanding of thermodynamics.

Accelerated Maximum Entropy Method for Time Series Models Estimation

The work is devoted to the development of a maximum entropy estimation method with soft randomization for restoring the parameters of probabilistic mathematical models from the available observations. Soft randomization refers to the technique of adding regularization to the functional of information entropy in order to simplify the optimization problem and speed up the learning process compared to the classical maximum entropy method. Entropic estimation makes it possible to restore probability distribution functions for model parameters without introducing additional assumptions about the likelihood function; thus, this estimation method can be used in problems with an unspecified type of measurement noise, such as analysis and forecasting of time series.