Phase coexistence in a weakly stochastic reaction-diffusion system

We investigate phase coexistence in a weakly stochastic reaction-diffusion system without assuming a continuum description. Concretely, for $(2N+1)$ diffusion-coupled vessels in which a chemical reaction exhibiting bistability occurs, we derive a condition for the phase coexistence in the limit $N \to \infty$. We then find that the phase coexistence condition depends on the rate of hopping between neighboring vessels. The conditions in the high- and low-hopping-rate limits are expressed in terms of two different potentials which are determined from the chemical reaction model in a single vessel.