# Quantum gravity effects in statistical mechanics with modified dispersion relation

## TL;DR

This paper investigates how quantum gravity-inspired modified dispersion relations and maximum energy/momentum scales affect the thermodynamics of photon gas using statistical mechanics, analyzing two different models.

## Contribution

It introduces the impact of deformed dispersion relations and upper bounds on thermodynamics, comparing two quantum gravity models.

## Key findings

- Modified dispersion relations alter photon gas thermodynamics.
- Upper bounds on energy/momentum influence partition functions.
- Distinct quantum gravity models produce different thermodynamic effects.

## Abstract

Planck scale inspired theories which are also often accompanied with maximum energy and/or momentum scale predict deformed dispersion relations compared to ordinary special relativity and quantum mechanics. In this paper we resort to the methods of statistical mechanics in order to determine the effects of a deformed dispersion relation along with upper bound in partition function as maximum energy and/or momentum scale can have on the thermodynamics of photon gas. We have analyzed two distinct quantum gravity models in this paper