Thermodynamics of blackbody radiation in nonlinear electrodynamics

We study the blackbody properties and the thermodynamic equilibrium quantities of a photon gas in the framework of nonlinear electrodynamics. In this vein, we take into account the photon propagation in a uniform external magnetic field in the weak field approximation, where an angular anisotropic energy density distribution appears in the frequency spectrum. The special case when the photon propagates perpendicular to the background magnetic field is also discussed, which allows us to probe the strong field regime. We then derive a modified blackbody spectral distribution and the Stefan-Boltzmann law in this situation. Considerations about Wien's displacement law and the Rayleigh-Jeans formula are contemplated as well. Deviations from the thermodynamic quantities at thermal equilibrium such as energy, pressure, entropy, and heat capacity densities are obtained from the Helmholtz free energy. As an application, we study three nonlinear electrodynamics, namely, the Euler-Heisenberg, the generalized Born-Infeld, and the logarithmic electrodynamics. Possible implications on stellar systems with strong magnetic fields such as magnetars are discussed.