Abstract: Deriving Fourier's law of heat conduction rigorously for deterministic heat conduction models is one of the big challenges in mathematical statistical physics. A promising direction is the two-step approach of Gaspard and Gilbert. We start with a system of finitely many interacting billiard particles governed by classical (deterministic) Newtonian mechanics, and in the first part, by tuning the geometry, we obtain a (stochastic) Markov interacting particle system in the "rare interaction limit". In the second part, we study the hydrodynamic limit of this stochastic system as the number of particles goes to infinity.

In this talk I present a small but important step in the second part of this program: the spectral gap of the appearing Markov process is shown to decay as 1/N^2 where N is the number of particles.

This is joint work with Eric Carlen and Gustavo Posta.