Maxwell-Juttner distributions in relativistic molecular dynamics

TL;DR

This paper investigates the validity of the molecular chaos hypothesis and Maxwell-Juttner distributions in relativistic molecular dynamics through a microscopic model, confirming their applicability in classical and ultrarelativistic regimes.

Contribution

It introduces a relativistic particle collision model to validate the molecular chaos hypothesis and Maxwell-Juttner distributions in relativistic kinetic theory.

Findings

Validation of the molecular chaos hypothesis in the model

Confirmation of Maxwell-Juttner distributions in the studied regimes

Derivation of temperature-kinetic energy relations in different regimes

Abstract

In relativistic kinetic theory, which underlies relativistic hydrodynamics, the molecular chaos hypothesis stands at the basis of the equilibrium Maxwell-Juttner probability distribution for the four-momentum $p^{\alpha}$. We investigate the possibility of validating this hypothesis by means of microscopic relativistic dynamics. We do this by introducing a model of relativistic colliding particles, and studying its dynamics. We verify the validity of the molecular chaos hypothesis, and of the Maxwell-Juttner distributions for our model. Two linear relations between temperature and average kinetic energy are obtained in classical and ultrarelativistic regimes.