Stochastic thermodynamics for kinetic equations

TL;DR

This paper develops a stochastic thermodynamics framework for kinetic equations, emphasizing the role of time-reversal odd variables and isotropic collision rates, and introduces a new fluctuation theorem demonstrated on a linear kinetic model.

Contribution

It introduces a stochastic thermodynamics formulation for odd variables and derives an alternative fluctuation theorem based solely on forward statistics.

Findings

Invariance under spatial rotation of collision rates is crucial.

An alternative detailed fluctuation theorem is derived.

The framework is illustrated with a linear kinetic equation with kangaroo rates.

Abstract

Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative detailed fluctuation theorem is derived, expressed solely in terms of forward statistics. It is illustrated for a linear kinetic equation with kangaroo rates.