The Boltzmann equation and equilibrium thermodynamics in Lorentz-violating theories

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.

Automated summary

In this study, we applied the principles of relativistic kinetic theory and the Boltzmann equation to particles with Lorentz-violating dispersion relations. We considered both classical (Maxwell-Boltzmann) and quantum (Fermi-Dirac and Bose-Einstein) statistics. Our results showed that Boltzmann's H-theorem still holds when the entropy current is appropriately defined. We derived equilibrium solutions and identified the effects of Lorentz violation on various thermodynamic variables and Bose-Einstein condensation. Additionally, we investigated a scenario involving nonelastic collisions between multiple species of particles, which corresponds to chemical or nuclear reactions.