Non-commutative correction of ideal gas thermodynamics

TL;DR

This paper explores how non-commutative geometry and Rainbow gravity modify the thermodynamics of an ideal relativistic gas, affecting black body radiation and specific heat calculations.

Contribution

It introduces a novel approach to incorporate $5$-deformed space-time and Rainbow gravity effects into the thermodynamics of ideal gases, providing new theoretical insights.

Findings

Modified black body radiation spectrum

Altered Debye theory of specific heat

Implications for relativistic thermodynamics

Abstract

In this study, we investigate the thermodynamics of a relativistic ideal within the context of $\kappa$-deformed space-time and Rainbow gravity background. To achieve this, we construct a modified partition function by considering a deformed Hamiltonian and incorporating corrections based on the time-invariant phase-space volume. We explore the implications of our model on the modified black body radiation spectrum and the modified Debye theory of specific heat in $\kappa$-deformed space-time and Rainbow gravity background.