Master equation and Fokker-Planck equation: Comparison of entropy and of rate constants

A usual approximation of the master equation is provided by the Fokker-Planck equation. For chemical systems with one species, we prove generally that the prediction of the rate constant of the metastable state given by the Master equation and the Fokker-Planck approximation differ exponentially with respect to the size of the system. We show that this is related to the fact that the entropy of the metastable state is not described correctly by the Fokker-Planck equation. We prove that the rate given by the Fokker-Planck equation overestimates that rate given by the Master equation.