The limit of mesoscopic one-way fluxes in a nonequilibrium chemical reaction with complex mechanism

Peng et al.(2020) formulated one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles. Species are classified into internal Y's and external X's. They defined the limit of mesoscopic one-way fluxes when the volume of the tank reactor tends to infinity as macroscopic one-way fluxes, but a rigorous proof of the existence of this limit is still awaiting. In this article, we fill this gap under a mild hypothesis: the Markov chain associated with the chemical master equation has finite states and any two rows in the stoichiometric matrices for the internal species Y's are not identical. In fact, an explicit expression of the limit is obtained.