Relativistic mass distribution in event-anti-event system and ``realistic'' equation of state for hot hadronic matter

We find the equation of state $p,\rho \propto T^6,$ which gives the value of the sound velocity $c^2=0.20,$ in agreement with the ``realistic'' equation of state for hot hadronic matter suggested by Shuryak, in the framework of a covariant relativistic statistical mechanics of an event--anti-event system with small chemical and mass potentials. The relativistic mass distribution for such a system is obtained and shown to be a good candidate for fitting hadronic resonances, in agreement with the phenomenological models of Hagedorn, Shuryak, {\it et al.} This distribution provides a correction to the value of specific heat 3/2, of the order of 5.5\%, at low temperatures.