  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.
