Generalized Stefan-Boltzmann law

TL;DR

This paper generalizes the classical thermodynamic derivation of the Stefan-Boltzmann law to various systems with zero chemical potential, unifying the thermodynamics of different non-interacting bosonic and fermionic gases.

Contribution

It provides a quantum-statistics-independent derivation applicable to diverse systems like Bose gases and Weyl Fermions, broadening the law's applicability.

Findings

Unified thermodynamic framework for bosonic and fermionic gases

Applicable to systems with vanishing chemical potential

Derivation independent of quantum statistics

Abstract

We reconsider the thermodynamic derivation by L. Boltzmann of the Stefan law and we generalize it for various different physical systems {\it whose chemical potential vanishes}. Being only based on classical arguments, therefore independent of the quantum statistics, this derivation applies as well to the saturated Bose gas in various geometries as to "compensated" Fermi gas near a neutrality point, such as a gas of Weyl Fermions. It unifies in the same framework the thermodynamics of many different bosonic or fermionic non-interacting gases which were until now described in completely different contexts.