https://doi.org/10.1140/epjp/s13360-023-03889-3
Regular Article
The Boltzmann equation and equilibrium thermodynamics in Lorentz-violating theories
1
Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal
2
Centro de Astrofísica e Gravitação, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001, Lisbon, Portugal
Received:
2
January
2023
Accepted:
10
March
2023
Published online:
18
April
2023
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.
© The Author(s) 2023
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