Fluctuation Theory in the Boltzmann–Grad Limit

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

doi:10.1007/s10955-020-02549-5

Fluctuation Theory in the Boltzmann–Grad Limit

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

École Polytechnique

PSL research University & IPSL
CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	873-895
Number of pages	23
Journal	Journal of Statistical Physics
Volume	180
Issue number	1-6
DOIs	https://doi.org/10.1007/s10955-020-02549-5
Publication status	Published - 1 Sept 2020

Keywords

Boltzmann equation
Fluctuations
Hard sphere dynamics
Kinetic theory
Large deviations
Low density limit
cumulants

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10.1007/s10955-020-02549-5

Cite this

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title = "Fluctuation Theory in the Boltzmann–Grad Limit",

abstract = "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.",

keywords = "Boltzmann equation, Fluctuations, Hard sphere dynamics, Kinetic theory, Large deviations, Low density limit, cumulants",

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N2 - 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.

AB - 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.

KW - Boltzmann equation

KW - Fluctuations

KW - Hard sphere dynamics

KW - Kinetic theory

KW - Large deviations

KW - Low density limit

KW - cumulants

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ER -

Fluctuation Theory in the Boltzmann–Grad Limit

Abstract

Keywords

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