Macroscopic stability of time evolution of Gibbs measures

TL;DR

This paper introduces properties called macroscopic mixing and transitive mixing to describe the stability of Gibbs measures over time, illustrating their relevance with a lattice mechanical system.

Contribution

It defines and demonstrates the importance of macroscopic mixing and transitive mixing as fundamental properties for macroscopic systems relaxing to equilibrium.

Findings

Lattice mechanical system exhibits these properties

Properties are fundamental for understanding relaxation to equilibrium

Provides a framework for macroscopic stability analysis

Abstract

We introduce two properties, macroscopic mixing and transitive mixing, to represent the macroscopic stability of time evolution of Gibbs measures. We claim that these are fundamental properties of macroscopic systems that exhibit relaxation to an equilibrium state. As an illustration, we show that a simple mechanical system on a lattice possesses these two properties.