Entropic Chaoticity for the Steady State of a Current Carrying System

TL;DR

This paper demonstrates that the steady state of a particle system under external influence and thermostats exhibits entropic chaoticity, with the distribution becoming increasingly independent across particles as system size grows.

Contribution

It establishes the entropic chaoticity of the steady state distribution for a particle system influenced by external fields and thermostats, extending previous notions of chaos.

Findings

The steady state forms a chaotic sequence as N increases.

The chaoticity property holds in the stronger entropic sense.

Explicit characterization of the steady state distribution in the small field limit.

Abstract

The steady state for a system of N particle under the influence of an external field and a Gaussian thermostat and colliding with random "virtual" scatterers can be obtained explicitly in the limit of small field. We show the sequence of steady state distribution, as N varies, forms a chaotic sequence in the sense that the k particle marginal, in the limit of large N, is the k-fold tensor product of the 1 particle marginal. We also show that the chaoticity properties holds in the stronger form of entropic chaoticity.