We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8408763 | PMC |
| http://dx.doi.org/10.1007/s11538-015-0102-8 | DOI Listing |
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