Entropy Production Bounds for the Kac Model are Uniform in the Number of Particles

In this paper, we prove fully quantitative entropy power law bounds for Kac’s collision model, uniform in the number of particles, by making use of the HWI inequality and Wasserstein distance power laws obtained by Rousset [34] via a Markovian coupling method. In turn, these bounds allow us to derive entropy power laws for the spatially homogeneous Boltzmann equation, akin to the results by Villani [40], by relatively elementary methods and requiring only moment and mild integrability conditions on the initial distribution.