Generalized kinetic theory of coarse-grained systems. I. Partial equilibrium and Markov approximations

IF 3.1 3区数学 Q1 MATHEMATICS

Advances in Difference Equations Pub Date : 2024-06-26 DOI:10.1186/s13662-024-03810-x

Bernard Gaveau, Michel Moreau

引用次数: 0

Abstract

The general kinetic theory of coarse-grained systems is presented in the abstract formalism of communication theory developed by Shannon and Weaver, Khinchin and Kolmogorov. The martingale theory shows that, under reasonable, general hypotheses, coarse-grained systems can be approximated by generalized Markov systems. For mixing systems, the Kolmogorov entropy production can be defined for nonstationary processes as Kolmogorov defined it for stationary processes.

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粗粒度系统的广义动力学理论。I. 局部平衡与马尔可夫近似

粗粒度系统的一般动力学理论是在香农和韦弗、辛钦和科尔莫戈罗夫发展的通信理论的抽象形式主义中提出的。鞅理论表明，在合理的一般假设条件下，粗粒度系统可以用广义马尔可夫系统来近似。对于混合系统，可以像科尔莫哥罗夫定义静止过程一样，定义非静止过程的科尔莫哥罗夫熵生成。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Difference Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

8.60

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.