Planck scale effect on the thermodynamics of photon gas

Abstract

A particular framework for quantum gravity is the doubly special relativity (DSR) formalism that introduces a new observer independent scale (the Planck scale). We resort to the methods of statistical mechanics in this framework to determine how the deformed dispersion relation affects the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, free energy and specific heat are calculated. These results are compared with the outcome obtained in the Lorentz violating model of Camacho and Marcias (Gen. Relativ. Gravit. 39: 1175-1183, 2007). The two types of models predict different results due to different spacetime structure near the Planck scale. The resulting modifications can be interpreted as a consequence of the deformed Lorentz symmetry present in the particular model we have considered. In the low energy limit, our calculation coincides with usual results of photon thermodynamics in special relativity (SR) theory, in contrast to the study presented in (Phys. Rev. D81, 085039 (2010)).