Fluctuation theory in the Boltzmann--Grad limit

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

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
4 CNRS - Centre National de la Recherche Scientifique

We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation. Deviations from this behaviour are described by dynamical correlations, which can be fully characterized for short times. This provides both a fluctuating Boltzmann equation and large deviation asymptotics.

Mots clés: large deviations; fluctuations; Boltzmann equation; hard-sphere gas

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella. Fluctuation theory in the Boltzmann--Grad limit. Journal of Statistical Physics, 2020, 180, pp.873-895. ⟨hal-02526608⟩