Large Deviations of Kac's Process & Applications

We consider the dynamical large deviations of an interacting particle system (Kac's process) whose hydrodynamic limit is the Boltzmann equation. In equilibrium, the particles are (at any given time) independent, and we recover the entropy from the large deviations at any one time. This gives us a new tool to investigate the entropy in the context of the Boltzmann equation, and we demonstrate some applications. One application will be a new derivation of Boltzmann's H-Theorem (decay of the entropy along the Boltzmann equation) from the reversibility of the microscopic dynamics.