2024-10-21 ジョージア工科大学
A pair of Smarticle robots from the lab of Prof. Dan Goldman. Earlier research from his group observed the arise of order in active matter from the physics of low rattling. (Photo Credit: Christa M. Ernst)
＜関連情報＞
- https://research.gatech.edu/rattling-physics-new-math
- https://www.pnas.org/doi/10.1073/pnas.2411731121
非平衡定常状態に対する局所-大域原理 A local–global principle for nonequilibrium steady states
Jacob Calvert and Dana Randall
Proceedings of the National Academy of Sciences Published:October 11, 2024
DOI:https://doi.org/10.1073/pnas.2411731121
Significance
Fundamentals of statistical physics explain that systems in thermal equilibrium exhibit spontaneous order because orderly configurations have low energy. This fact is remarkable, and powerful, because energy is a “local” property of configurations. Nonequilibrium systems, including engineered and living systems, can also exhibit order, but there is no property analogous to energy that generally explains why orderly configurations of these systems often emerge. However, recent experiments suggest that a local property called “rattling” predicts which configurations are favored, at least for a broad class of nonequilibrium systems. We develop a theory of rattling that explains for which systems it works and why, and we demonstrate its application across scientific domains.
Abstract
The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization 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.
