Equilibrium and Termination ( extended version ) ∗

We present a reduction of the Post correspondence problem (PCP) to the question of whether a continuous-time Markov chain (CTMC) presented as a set graph-rewriting rules has an equilibrium. It follows that the question of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable. The encoding uses the Kappa language and is presented in details for a simple PCP instance in the Appendix.