Decay of Entropy and Information of multidimensional Kac models coupled to large systems

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 investigate the Kac system coupled to a thermostat, and secondly connected to a heat reservoir. As a result, we obtain exponential decay rates for the entropy and information that are essentially independent of the size of the systems. The use of the Fisher-information allows simple proofs with weak regularity assumptions.