Equilibrium and termination II: the case of Petri nets

Abstract

This paper is concerned with the asymptotic properties of a restricted class of Petri nets equipped with stochastic mass-action semantics. We establish a simple algebraic criterion for the existence of an equilibrium, that is to say, an invariant probability that satisfies the detailed balance condition familiar from the thermodynamics of reaction networks. We also find that when such a probability exists, it can be described by a free energy function that combines an internal energy term and an entropy term. Under strong additional conditions, we show how the entropy term can be deconstructed using the finer-grained individual-token semantics of Petri nets.