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.

References in corpus (4)

• Macroscopic fluctuation theory
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Abstract cluster expansion with applications to statistical mechanical systems
• The Boltzmann-Grad Limit of a Hard Sphere System: Analysis of the Correlation Error

Cited by in corpus (11)

• Is the Boltzmann equation reversible? A large deviation perspective on the irreversibility paradox
• A new approach to the mean-field limit of Vlasov-Fokker-Planck equations
• Dynamical large deviations for homogeneous systems with long range interactions and the Balescu--Guernsey--Lenard equation
• Large deviations for Kac-like walks
• A new spectral analysis of stationary random Schrödinger operators
• Propagation processes of correlations of hard spheres
• Dynamical large deviations for plasmas below the Debye length and the Landau equation
• Cluster expansion for a dilute hard sphere gas dynamics
• Dynamical large deviations for an inhomogeneous wave kinetic theory: linear wave scattering by a random medium
• Non-perturbative solutions of hierarchies of evolution equations for colliding particles
• Macroscopic dynamical fluctuations in Kac ring model