Entropy Decay for the Kac Master Equation

Entropy Decay for the Kac Master Equation

Michael Loss, Georgia Institute of Technology

The Kac master equation models the behavior of a large number of randomly colliding particles. Due to its simplicity it allows, without too much pain, to investigate a number of issues. E.g., Mark Kac, who invented this model in 1956, used it to give a simple derivation of the spatially inhomogeneous Boltzmann equation. One important issue is the rate of approach to equilibrium, which can be analyzed in various ways, using, e.g., the gap or the entropy. Explicit entropy estimates will be discussed for a Kac type master equation modeling the interaction of a nite system with a large but nite reservoir. This is joint work with Federico Bonetto, Alissa Geisinger and Tobias Ried.