Relativistic Quantum Thermodynamics of Ideal Gases in 2 Dimensions

TL;DR

This paper investigates the thermodynamic properties of relativistic ideal Bose and Fermi gases in two dimensions, deriving unified density expressions and highlighting their fundamental differences from non-relativistic cases.

Contribution

It provides a unified analytical framework for relativistic gases in 2D and clarifies their inequivalence, contrasting with non-relativistic limits.

Findings

Derived closed-form densities using polylogarithms

Established fundamental differences between Bose and Fermi gases in relativistic regime

Showed non-equivalence of spinless, equal-mass gases in relativistic case

Abstract

In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.