Entropy bound for the photon gas in noncommutative spacetime

TL;DR

This paper investigates the thermodynamics of a photon gas in noncommutative spacetime, deriving entropy and energy bounds influenced by quantum gravity effects, with implications for black hole entropy.

Contribution

It introduces a model for photon gas thermodynamics in noncommutative spacetime with compact momentum space, deriving bounds related to Planck scale physics.

Findings

Maximum internal energy is of the order of Planck energy.

Entropy bound scales with the volume and Planck length.

Thermodynamics resembles black hole entropy behavior.

Abstract

Motivated by the doubly special relativity theories and noncommutative spacetime structures, thermodynamical properties of the photon gas in a phase space with compact spatial momentum space is studied. At the high temperature limit, the upper bounds for the internal energy and entropy are obtained which are determined by the size of the compact spatial momentum space. The maximum internal energy turns out to be of the order of the Planck energy and the entropy bound is then determined by the factor $\big(V/l_{_{\rm Pl}}^3\big)$ through the relevant identification of the size of the momentum space with Planck scale. The entropy bound is very similar to the case of Bekenstein-Hawking entropy of black holes and suggests that thermodynamics of black holes may be deduced from a saturated state in the framework of a full quantum gravitational statistical mechanics.