A local-global principle for nonequilibrium steady states

• 成果类型: Article
• 署名作者: Calvert, Jacob; Randall, Dana
• 署名单位: University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-11571
• DOI: 10.1073/pnas.2411731121
• 发表日期: 2024-10-15
• 关键词: free-energy differences; fluctuation theorem; entropy production; solvable model; equilibrium

摘要

The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of selforganization because energy is a local property of configurations. For nonequilibrium systems, there is no such property for which an analogous principle holds, hence no common explanation of the diverse forms of self-organization they exhibit. However, a flurry of recent empirical results has shown that a local property of configurations called rattling predicts the steady states of some nonequilibrium systems, leading to claims of a far-reaching principle of nonequilibrium self-organization. But for which nonequilibrium systems is rattling accurate, and why? We develop a theory of rattling in terms of Markov processes that gives simple and precise answers to these key questions. Our results show that rattling predicts a broader class of nonequilibrium steady states than has been claimed and for different reasons than have been suggested. Its predictions hold to an extent determined by the relative variance of, and correlation between, the local and global parts of a steady state. We show how these quantities characterize the local-global relationships of various random walks on random graphs, spin-glass dynamics, and models of animal collective behavior. Surprisingly, we find that the core idea of rattling is so general as to apply to equilibrium and nonequilibrium systems alike.