Maxwell-Jüttner distributions in relativistic molecular dynamics

Abstract

In relativistic kinetic theory, which underlies relativistic hydrodynamics, the molecular chaos hypothesis stands at the basis of the equilibrium Maxwell-J $\ddot{\mbox{u}}$ ttner probability distribution for the four-momentum pα. 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-J $\ddot{\mbox{u}}$ ttner distributions for our model. Two linear relations between temperature and average kinetic energy are obtained in classical and ultrarelativistic regimes.