We present a reduction of the Post correspondence problem to the
question of whether a continuoustime Markov chain has an
equilibrium. It follows that whether a computable CTMC is dissipative
(ie does not have an equilibrium) is undecidable, and more generally
equilibrium can be seen as a form of sequential termination. We
generalize this idea to a class of reversible communicating
processes. Transition rates are derived from a formal notion of
energy which increases exponentially with the size of the local
history of a process. This second construction can be seen as a
concurrent version of the MetropolisHastings algorithm.
