Equilibrium Relativistic Mass Distribution

The relativistic Maxwell-Boltzmann distribution for the system of $N$ events with motion in space-time parametrized by an invariant ``historical time’’ $\tau$ is considered without the simplifying approximation $m^2\cong M^2$, where $M$ is a given intrinsic property of the events. The relativistic mass distribution is obtained and the average values of $m$ and $m^2$ are calculated. The average value of the energy in nonrelativistic limit gives a correction of the order of 10% to the Dulong-Petit law. Expressions for the pressure and the density of events are obtained and the ideal gas law is recovered.