Equilibrium Relativistic Mass Distribution for Indistinguishable Events

A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau$ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperbolic angular variables. All the characteristic averages are calculated. Expressions for the pressure and the density of events are found and the relativistic equation of state is obtained. The Galilean limit is considered; the theory is shown to pass over to the usual nonrelativistic statistical mechanics of indistinguishable particles.