Abstract
One can often extract valuable properties of Markov chains (MCs) by “compressing” them using various notions of bisimulation (exact or approximate, strong or weak, etc) [10,3,2,4]. Typically a bisimulation will lead from a concrete and perhaps overly detailed system to a simpler and more abstract one [7]. In this paper, we will go the opposite way! We will show that for the subclass of continuous-time MCs (ctMCs) corresponding to thermodynamically consistent stochastic mass action Petri nets (the standard model for chemical reactions for fast diffusing chemicals), one can construct in a systematic fashion concrete versions of the dynamics. These concrete MCs are functionally bisimilar to their abstract counterpart and admit a simpler description of their invariant probability (equivalently, of their energy function). This can sometimes reveal interesting equilibrium properties of the original chain.
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