Effect of Non-commutativity of space-time on Thermodynamics of Photon gas

TL;DR

This paper investigates how the non-commutative structure of space-time in doubly special relativity affects the thermodynamics of photon gases, revealing deviations from classical results at quantum gravity scales.

Contribution

It presents the first analysis of photon gas thermodynamics within the $ {k}$-Minkowski space-time framework considering first-order deformation effects.

Findings

Deformation modifies photon gas thermodynamics at quantum scales

Results recover standard thermodynamics as deformation parameter approaches zero

Provides insights into quantum gravity effects on thermodynamic systems

Abstract

Doubly special relativity(DSR) introduce a minimal length scale i.e. the Planck length scale, which is independent length scale in addition to the speed of light in the normal special theory of relativity(STR). Doubly special relativity leads to study the $\kappa$-Minkowski space-time. In this paper, we present the result of our investigation on the thermodynamics of photon gas in the $\kappa$-Minkowski space-time. For studying this, we start with the $\kappa$-deformed dispersion relation and keep terms upto first order in the deformation parameter $a$ and we study that how does $\kappa$-deformed dispersion relation affect the thermodynamics of photon gas. In the limit, deformation parameter $a \rightarrow 0$, we get back all the results in the special theory of relativity(STR)\cite{partition}.