Maxwell-Jüttner distributions in relativistic molecular dynamics

In relativistic kinetic theory, which underlies relativistic hydrodynamics, the molecular chaos hypothesis stands at the basis of the equilibrium Maxwell-J<InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\ddot{\mbox{u}}$</EquationSource> </InlineEquation>ttner probability distribution for the four-momentum p<Superscript>α</Superscript>. 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<InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\ddot{\mbox{u}}$</EquationSource> </InlineEquation>ttner distributions for our model. Two linear relations between temperature and average kinetic energy are obtained in classical and ultrarelativistic regimes. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006