Photon gas thermodynamics in dS and AdS momentum spaces

TL;DR

This paper explores the thermodynamics of photon gases within deformed special relativity models based on de Sitter and anti-de Sitter momentum spaces, revealing dual thermodynamic limits and symmetry-breaking effects.

Contribution

It introduces a thermodynamic analysis of photon gases in dS and AdS momentum spaces, highlighting the duality and maximal thermodynamic quantities in these models.

Findings

Maximal pressure and temperature in dS model.

Maximal internal energy and entropy in AdS model.

Thermodynamic duality between the models.

Abstract

In this paper, we study thermostatistical properties of a photon gas in the framework of two deformed special relativity models defined by the cosmological coordinatizations of the de Sitter (dS) and anti-de Sitter (AdS) momentum spaces. The dS model is a doubly special relativity theory in which an ultraviolet length scale is invariant under the deformed Lorentz transformations. For the case of AdS model, however, the Lorentz symmetry breaks at the high energy regime. We show that the existence of a maximal momentum in dS momentum space leads to maximal pressure and temperature at the thermodynamical level while maximal internal energy and entropy arise for the case of the AdS momentum space due to the existence of a maximal kinematical energy. These results show the thermodynamical duality of these models much similar to their well-known kinematical duality.