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非线性福克-普朗克方程、H定理与复合系统的广义熵

Nonlinear Fokker-Planck Equations, H-Theorem and Generalized Entropy of a Composed System.

作者信息

Evangelista Luiz R, Lenzi Ervin K

机构信息

Dipartimento di Scienza Applicata e Tecnologia (DISAT) del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Istituto dei Sistemi Complessi del Consiglio Nazionale delle Ricerche (ISC-CNR) co Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

出版信息

Entropy (Basel). 2023 Sep 20;25(9):1357. doi: 10.3390/e25091357.

DOI:10.3390/e25091357
PMID:37761656
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10528951/
Abstract

We investigate the dynamics of a system composed of two different subsystems when subjected to different nonlinear Fokker-Planck equations by considering the H-theorem. We use the H-theorem to obtain the conditions required to establish a suitable dependence for the system's interaction that agrees with the thermodynamics law when the nonlinearity in these equations is the same. In this framework, we also consider different dynamical aspects of each subsystem and investigate a possible expression for the entropy of the composite system.

摘要

我们通过考虑H定理,研究了由两个不同子系统组成的系统在受到不同非线性福克 - 普朗克方程作用时的动力学。当这些方程中的非线性相同时,我们使用H定理来获得建立与热力学定律相符的系统相互作用的合适依赖关系所需的条件。在此框架下,我们还考虑了每个子系统的不同动力学方面,并研究了复合系统熵的可能表达式。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4226/10528951/2dc49e7c073a/entropy-25-01357-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4226/10528951/a6874c3d0ce9/entropy-25-01357-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4226/10528951/2dc49e7c073a/entropy-25-01357-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4226/10528951/a6874c3d0ce9/entropy-25-01357-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4226/10528951/2dc49e7c073a/entropy-25-01357-g002.jpg

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本文引用的文献

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Nonequilibrium distributions from the Fokker-Planck equation: Kappa distributions and Tsallis entropy.福克-普朗克方程的非平衡分布:κ分布与Tsallis熵。
Phys Rev E. 2023 Jul;108(1-1):014111. doi: 10.1103/PhysRevE.108.014111.
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A Review of Fractional Order Entropies.分数阶熵综述
Entropy (Basel). 2020 Dec 5;22(12):1374. doi: 10.3390/e22121374.
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Extensions and solutions for nonlinear diffusion equations and random walks.非线性扩散方程与随机游走的扩展及解
Entropy (Basel). 2024 May 7;26(5):406. doi: 10.3390/e26050406.
4
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Entropy (Basel). 2023 Nov 23;25(12):1578. doi: 10.3390/e25121578.
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Entropy production and nonlinear Fokker-Planck equations.熵产生与非线性福克 - 普朗克方程。
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 1):061136. doi: 10.1103/PhysRevE.86.061136. Epub 2012 Dec 27.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Oct;76(4 Pt 1):041123. doi: 10.1103/PhysRevE.76.041123. Epub 2007 Oct 17.
8
Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.非线性反常扩散方程与分形维数:精确广义高斯解
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