Time-reversal symmetry relation for nonequilibrium flows ruled by the fluctuating Boltzmann equation

TL;DR

This paper derives a time-reversal symmetry relation for nonequilibrium dilute gases described by the fluctuating Boltzmann equation, linking particle and energy current fluctuations to fundamental symmetries.

Contribution

It introduces a novel symmetry relation for fluctuating particle and energy currents in gases governed by the fluctuating Boltzmann equation, extending nonequilibrium statistical mechanics.

Findings

Establishes a time-reversal symmetry relation for fluctuating currents.

Connects microscopic dynamics to macroscopic fluctuation properties.

Provides a theoretical foundation for analyzing nonequilibrium gas flows.

Abstract

A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random numbers of particles in cells of given position and velocity in the single-particle phase space. The symmetry relation concerns the fluctuating particle and energy currents of the gas flowing between reservoirs or thermalizing surfaces at given particle densities or temperatures.