Photon Gas at the Planck Scale within the Doubly Special Relativity

TL;DR

This paper explores the thermodynamics of photon gas within doubly special relativity, introducing a new energy addition rule and analyzing black-body radiation behavior at the Planck scale.

Contribution

It proposes a novel $ppa$-addition rule for energies in DSR and investigates its implications for photon gas thermodynamics and black-body radiation.

Findings

Finite entropy for one-mode subsystem.

Existence of a threshold temperature for radiation.

Modified thermodynamic behavior at the Planck scale.

Abstract

Within the approach to doubly special relativity (DSR) suggested by Magueijo and Smolin, a new algebraically justified rule of so-called $\kappa$-addition for the energies of identical particles is proposed. This rule permits to introduce the nonlinear $\kappa$-dependent Hamiltonian for one-mode multi-photon (sub)system. On its base, with different modes treated as independent, the thermodynamics of black-body radiation is explored within DSR, and main thermodynamic quantities are obtained. In their derivation, we use both the analytical tools within mean field approximation (MFA) and numerical evaluations based on exact formulas. The entropy of one-mode subsystem turns out to be finite (bounded). Another unusual result is the existence of threshold temperature above which radiation is present. Specific features of the obtained results are explained and illustrated with a number of plots. Comparison with some works of relevance is given.