Equilibrium and Termination

We present a reduction of the Turing halting problem (in the simplified form of the Post correspondence problem) to the problem of whether a continuous-time Markov chain (CTMC) presented as a set of Kappa graph-rewriting rules has an equilibrium. It follows that the problem of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable.