A Statistical Mechanical Model for Mass Stability in the SHP Theory
  We construct a model for a particle in the framework of the theory of Stueckelberg, Horwitz and Piron (SHP) as an ensemble of events subject to the laws of covariant classical equilibrium statistical mechanics. The canonical and grand canonical emsembles are constructed without an a priori constraint on the total mass of the system. We show that the total mass of the system, corresponding to the mass of this particle, is determined by a chemical potential. This model has the property that under perturbation, such as collisions in the SHP theory for which the final asymptotic mass of an elementary event is not constrained by the basic theory, the particle returns to its equilibrium mass value. A mechanism similar to the Maxwell construction for more than one equlibrium mass state may result in several possible masses in the final state. 
Lawrence Horwitz
physics.class-ph hep-th