Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Mar;79(3):031124. doi: 10.1103/PhysRevE.79.031124. Epub 2009 Mar 30.

Statistical thermodynamics of a two-dimensional relativistic gas.

Physical review. E, Statistical, nonlinear, and soft matter physics

Afshin Montakhab, Malihe Ghodrat, Mahmood Barati

PMID: 19391919 DOI: 10.1103/PhysRevE.79.031124

Abstract

In this paper 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 Jüttner 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).

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• Journal Article