Ultrarelativistic Bose–Einstein gas on Lorentz symmetry violation

In this paper, we study the effects of Lorentz Symmetry Breaking on the thermodynamic properties of ideal gases. Inspired by the dispersion relation coming from the Carroll–Field–Jackiw model for Electrodynamics with Lorentz and CPT violation term, we compute the thermodynamics quantities for a Boltzmann, Fermi–Dirac and Bose–Einstein distributions. Two regimes are analyzed: the large and the small Lorentz violation. In the first case, we show that the topological mass induced by the Chern–Simons term behaves as a chemical potential. For Bose–Einstein gases, a condensation in both regimes can be found.