Long-time derivation at equilibrium of the fluctuating Boltzmann equation

Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella

Published 2022-01-12Version 1

We study a hard sphere gas at equilibrium, and prove that in the low density limit, the fluctuations converge to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times. The method of proof builds upon the weak convergence method introduced in the companion paper [8] which is improved by considering clusters of pseudo-trajectories as in [7].