The Relativistic Boltzmann Equation and Two Times

We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter [Formula: see text]. The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of [Formula: see text]. If [Formula: see text] increases with [Formula: see text] , the worldline may be associated with a normal particle, but if it is decreasing in [Formula: see text] , it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time.