Decay of Entropy and Information for multidimensional Kac models

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.