Universal relation between thermodynamic driving force and one-way fluxes in a nonequilibrium chemical reaction with complex mechanism

Abstract

In nonequilibrium chemical reaction systems, a fundamental relationship between unbalanced kinetic one-way fluxes and thermodynamic chemical driving forces is believed to exist. However, in fact, the formula for this fundamental relation, in general, and the very definition of kinetic one-way fluxes in nonlinear chemical reaction networks, are still missing. In terms of its stochastic kinetic representation, we formulate the one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles. For each kinetic cycle, the logarithm of the ratio of the steady-state forward and backward one-way fluxes is equal to the free energy difference between the reactants and products along the cycle. This fundamental relation is further established for general chemical reaction networks with multiple input and output complexes. This work provides a concrete mathematical/physical basis for a long-hold belief in chemical kinetics. It gives an equivalent definition of the free energy difference in nonequilibrium chemical reaction networks and unifies the stochastic and macroscopic nonequilibrium chemical thermodynamics in a very broad setting.