On the statistical thermodynamics of reversible communicating processes

Abstract

We propose a probabilistic interpretation of a class of reversible communicating processes. The rate of forward and backward computing steps, instead of being given explicitly, is derived from a set of formal energy parameters. This is similar to the Metropolis-Hastings algorithm. We find a lower bound on energy costs which guarantees that a process converges to a probabilistic equilibrium state (a grand canonical ensemble in statistical physics terms [19]). This implies that such processes hit a success state in finite average time, if there is one. © 2011 Springer-Verlag.