Sub-exponential mixing of open systems with particle-disk interactions

TL;DR

This paper studies a class of particle systems with deterministic interactions and heat reservoirs, proving the existence of a unique steady state that is mixing but not exponentially, with convergence rates that can be sub-exponential.

Contribution

It establishes the existence, uniqueness, and mixing properties of the steady state in particle-disk systems with heat reservoirs, including sub-exponential convergence rates.

Findings

Unique non-equilibrium steady state exists.

Steady state is mixing but not exponentially.

Convergence to steady state can be sub-exponential.

Abstract

We consider a class of mechanical particle systems with deterministic particle-disk interactions coupled to Gibbs heat reservoirs at possibly different temperatures. We show that there exists a unique (non-equilibrium) steady state. This steady state is mixing, but not exponentially mixing, and all initial distributions converge to it. In addition, for a class of initial distributions, the rates of converge to the steady state are sub-exponential.