Ergodicity of some open systems with particle-disk interactions

TL;DR

This paper proves that certain open mechanical systems with particle-disk interactions connected to heat baths have unique, ergodic steady states that are absolutely continuous, under natural assumptions.

Contribution

It establishes ergodicity and uniqueness of steady states for a class of particle-disk systems coupled to heat baths, extending understanding of their long-term behavior.

Findings

Steady states are ergodic and absolutely continuous.

At most one such steady state exists.

Results apply under natural assumptions.

Abstract

We consider steady states for a class of mechanical systems with particle-disk interactions coupled to two, possibly unequal, heat baths. We show that any steady state that satisfies some natural assumptions is ergodic and absolutely continuous with respect to a Lebesgue-type reference measure and conclude that there exists at most one absolutely continuous steady state.