The Boltzmann equation and equilibrium thermodynamics in Lorentz-violating theories

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 nonelastic collisions between multiple species of particles corresponding to chemical or nuclear reactions is considered.