Universal Relation Between Thermodynamic Driving Force and One-Way Fluxes in a Nonequilibrium Chemical Reaction with Complex Mechanism

In nonequilibrium chemical reaction systems, a fundamental relationship between unbalanced kinetic one-way fluxes and thermodynamic chemical driving forces is believed to exists. However this relation has been rigorously demonstrated only in a few cases in which one-way fluxes are well defined. 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. Our result not only provides an equivalent definition of free energy difference in nonequilibrium chemical reaction networks, it also unifies the stochastic and macroscopic nonequilibrium chemical thermodynamics in a very broad sense.