Long-time derivation at equilibrium of the fluctuating Boltzmann equation

Thierry Bodineau (1) , Isabelle Gallagher (2) , Laure Saint-Raymond (3) , Sergio Simonella (4)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 IHES - Institut des Hautes Études Scientifiques
4 ENS de Lyon - École normale supérieure de Lyon

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].

Mots clés: Hard sphere gas; Boltzmann Equation; Fluctuating field

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella. Long-time derivation at equilibrium of the fluctuating Boltzmann equation. 2022. ⟨hal-03519557⟩