Statistical thermodynamics of a two dimensional relativistic gas

TL;DR

This study uses molecular dynamics to analyze a two-dimensional relativistic gas, confirming the Jüttner distribution as the correct velocity distribution and exploring the complexities of temperature transformation in relativistic thermodynamics.

Contribution

It introduces a fully relativistic 2D hard-disk gas model and investigates velocity distributions and temperature transformation, addressing unresolved issues in relativistic thermodynamics.

Findings

Jüttner distribution correctly generalizes Maxwell-Boltzmann in relativistic context

Same temperature parameter β observed in both rest and moving frames

Local thermal equilibrium exists in the moving frame, but temperature transformation remains inconclusive

Abstract

In this article we study a fully relativistic model of a two dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects in statistical thermodynamics. We study this model using molecular-dynamics simulation, concentrating on the velocity distribution functions. We obtain results for $x$ and $y$ components of velocity in the rest frame ($\Gamma$) as well as the moving frame ($\Gamma'$). Our results confirm that J\"{u}ttner distribution is the correct generalization of Maxwell-Boltzmann distribution. We obtain the same "temperature" parameter $\beta$ for both frames consistent with a recent study of a limited one-dimensional model. We also address the controversial topic of temperature transformation. We show that while local thermal equilibrium holds in the moving frame, relying on statistical methods such as distribution functions or equipartition theorem are ultimately inconclusive in deciding on a correct temperature transformation law (if any).