源自统计物理的数学论题——统计物理与概率的交叉  

Mathematical topics motivated from statistical physics——Interaction of statistical physics and probability theory

作　　者：陈木法[1] Mufa Chen

机构地区：[1]北京师范大学数学科学学院

出　　处：《中国科学：数学》2020年第1期3-14,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11771046)资助项目

摘　　要：从数学上讲,本文介绍从Markov链到非平衡交互作用粒子系统的发展;从物理上讲,这是从平衡态统计力学到非平衡态统计物理的新进程.本文介绍从中开发出来的几个典型成果和数学工具.包括平衡态与非平衡态模型的判别,非平衡态模型的数学构造、基本性质研究及概率度量和耦合方法等.In mathematical language, the paper introduces the development from Markov chains to the nonequilibrium interacting particle systems. In physical language, it is a way motivated from equilibrium statistical physics to nonequilibrium. Mainly, some typical results and mathematical tools developed in period are introduced, including the criteria of equibibrium/nonequilibrium, the construction and further property of a typical class of nonequilibrium system-the reaction-diffusion processes, as well as the important tools-probability metrics and coupling.

关 键 词：MARKOV链 交互作用粒子系统 反应扩散过程 平衡态与非平衡态 

分 类 号：O414.2[理学—理论物理] O211[理学—物理]