The Boltzmann equation and equilibrium thermodynamics in Lorentz-violating theories

TL;DR

This paper extends relativistic kinetic theory and the Boltzmann equation to Lorentz-violating particles, analyzing their thermodynamic behavior and equilibrium states within the Standard-Model Extension framework.

Contribution

It adapts the Boltzmann equation to Lorentz-violating dispersion relations and explores thermodynamics, including Bose-Einstein condensation and multi-species reactions.

Findings

Boltzmann's H-theorem remains valid with Lorentz violation.

Derived equilibrium solutions showing Lorentz-violating effects.

Analyzed thermodynamics for classical and quantum statistics.

Abstract

In this work we adapt the foundations of relativistic kinetic theory and the Boltzmann equation to particles with Lorentz-violating dispersion relations. The latter are taken to be those associated to two commonly considered sets of coefficients in the minimal Standard-Model Extension. We treat both the cases of classical (Maxwell-Boltzmann) and quantum (Fermi-Dirac and Bose-Einstein) statistics. It is shown that with the appropriate definition of the entropy current, Boltzmann's H-theorem continues to hold. We derive the equilibrium solutions and then identify the Lorentz-violating effects for various thermodynamic variables, as well as for Bose-Einstein condensation. Finally, a scenario with non-elastic collisions between multiple species of particles corresponding to chemical or nuclear reactions is considered.