Thermodynamics of a photon gas and deformed dispersion relations

TL;DR

This paper investigates how deformed dispersion relations, indicating Lorentz invariance breakdown, affect the thermodynamics of a photon gas, revealing increased entropy and photon interactions.

Contribution

It introduces a novel analysis of photon gas thermodynamics under deformed dispersion relations, linking Lorentz symmetry loss to thermodynamic modifications.

Findings

Deformed dispersion relations modify the density of states and thermodynamic quantities.

Lorentz invariance breakdown acts as a repulsive photon interaction.

Entropy increases due to the growth in microstates from symmetry loss.

Abstract

We resort to the methods of statistical mechanics in order to determine the effects that a deformed dispersion relation has upon the thermodynamics of a photon gas. The ensuing modifications to the density of states, partition function, pressure, internal energy, entropy, and specific heat are calculated. It will be shown that the breakdown of Lorentz invariance can be interpreted as a repulsive interaction, among the photons. Additionally, it will be proved that the presence of a deformed dispersion relation entails an increase in the entropy of the system. In other words, as a consequence of the loss of the aforementioned symmetry the number of microstates available to the corresponding equilibrium state grows.