Decay of Entropy and Information for multidimensional Kac models

Abstract

We study the approach to equilibrium in relative entropy of systems of gas particles modeled via 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 simple proofs with weak regularity assumptions. As a result, we obtain exponential decay rates for the entropy and information that are essentially independent of the size of the systems.