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

Statistical thermodynamics of a two dimensional relativistic gas