Molecular dynamics simulation of a relativistic gas: Thermostatistical properties

Studying special relativistic generalizations of classical thermodynamic systems have recently attracted much attention despite its long and controversial history. Here, we propose a relativistic model of a realistic dilute gas which can easily be studied using standard molecular dynamics simulations. We briefly outline some of its thermostatistical properties which help resolve controversial issues in relativistic thermodynamics. In particular, we find that Jüttner function is the correct generalization of Maxwell–Boltzmann velocity distribution. We also conclude that relativistic temperature is best understood as a rest-frame-property, invariant under various relativistic transformations, i.e. Lorentz transformation and time reparametrization. Finally, we provide canonical non-equilibrium simulations of such systems and study the effects of a temperature gradient imposed by heat reservoirs.