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Peng et al.(2020) formulated one-way fluxes for a general chemical reactionfar from equilibrium, with arbitrary complex mechanisms, multipleintermediates, and internal kinetic cycles. Species are classified intointernal Y's and external X's. They defined the limit of mesoscopic one-wayfluxes when the volume of the tank reactor tends to infinity as macroscopicone-way fluxes, but a rigorous proof of the existence of this limit is stillawaiting. In this article, we fill this gap under a mild hypothesis: the Markovchain associated with the chemical master equation has finite states and anytwo rows in the stoichiometric matrices for the internal species Y's are notidentical. In fact, an explicit expression of the limit is obtained.

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