Abstract
In this paper we analyze the thermodynamic properties of a photon gas under the influence of a background electromagnetic field in the context of any nonlinear electrodynamics. Neglecting the self-interaction of photons, we obtain a general expression for the grand canonical potential. Particularizing for the case when the background field is uniform, we determine the pressure and the energy density for the photon gas. Although the pressure and the energy density change when compared with the standard case, the relationship between them remains unaltered, namely ρ=3p. Finally, we apply the developed formulation to the cases of Heisenberg–Euler and Born–Infeld nonlinear electrodynamics. For the Heisenberg–Euler case, we show that our formalism recovers the results obtained with the 2-loop thermal effective action approach.
Highlights
Maxwell electrodynamics is one of the most successful theories in the history of physics
A third example where nonlinear electrodynamics (NLED) models appear is in the description of radiation propagation inside specific materials
Modified dispersion relations appear in deformed special relativity (DSR) models and in NLED scenarios. This interesting effect occurs in NLED when we study wave propagation in an electromagnetic background
Summary
Maxwell electrodynamics is one of the most successful theories in the history of physics. A third example where NLED models appear is in the description of radiation propagation inside specific materials In these cases, we usually do not have a Lagrangian approach but the nonlinear effects emerge through nonconstant constitutive relations [26,27,28,29]. In the context of deformed special relativity (DSR), some papers have studied thermodynamics consequences of modifications in the relativistic dispersion relation [30,31,32,33] These works are usually motivated by the possibility of Lorentz symmetry breakdown at Planck scales [34, 35]. Modified dispersion relations appear in DSR models and in NLED scenarios This interesting effect occurs in NLED when we study wave propagation in an electromagnetic background. A discussion about the birefringence phenomenon is presented in Appendix A
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