Entropy Production along Dominant Pathway of Nonequilibrium Phase Transition in Mesoscopic Chemical System

We consider a bistable mesoscopic chemical reaction system and calculate entropy produc-tion along the dominant pathway during nonequilibrium phase transition. Using probability generating function method and eikonal approximation, we first convert the chemical master equation into the classical Hamilton-Jacobi equation, and then find the dominant pathways between two steady states in the phase space by calculating zero-energy trajectories. We find that entropy productions are related to the actions of the forward and backward dominant pathways. At the coexistence point where the stabilities of the two steady states are equiv-alent, both the system entropy change and the medium entropy change are zero; whereas at non-coexistence point both of them are nonzero.