Decay of Entropy and Information for multidimensional Kac models

TL;DR

This paper investigates how systems of gas particles modeled by the multidimensional Kac master equation approach equilibrium, demonstrating exponential decay of entropy and information with rates largely unaffected by system size.

Contribution

It introduces elementary proofs using Fisher-information to show exponential decay of entropy and information in Kac models coupled to thermostats or heat reservoirs, in arbitrary dimensions.

Findings

Exponential decay rates for entropy and information are established.

Decay rates are essentially independent of system size.

Elementary proofs require only weak regularity assumptions.

Abstract

We study the approach to equilibrium of systems of gas particles in terms of relative entropy. The systems are modeled by the Kac master equation in arbitrary dimensions. First, we study the Kac system coupled to a thermostat, and secondly connected to a heat reservoir. The use of the Fisher-information allows elementary proofs with weak regularity assumptions. As a result, we obtain for both systems exponential decay rates for the entropy and information that are essentially independent of the size of the systems.