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

TL;DR

This paper rigorously proves the existence and provides an explicit expression for the macroscopic limit of mesoscopic one-way fluxes in complex nonequilibrium chemical reactions, extending Peng et al.'s 2020 formulation.

Contribution

It establishes the rigorous existence of the flux limit and derives an explicit formula under mild conditions, advancing the theoretical understanding of complex reaction mechanisms.

Findings

Proved the existence of the flux limit in complex reactions.

Derived an explicit expression for the macroscopic flux.

Validated the limit under finite Markov chain states.

Abstract

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.