Abstract
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.
Highlights
In the terminology of classical mechanics, chemical kinetics and thermodynamics correspond to kinematics and dynamics, respectively [1]
We show a universal relationship between kinetic fluxes and thermodynamic driving forces in a nonequilibrium chemical reaction network (CRN), which are key concepts in the respective theories
The one-way flux of each reaction cycle is defined through the cycle fluxes in the counting space of the corresponding chemical-master-equation model [14] describing the stochastic kinetics of molecular numbers
Summary
In the terminology of classical mechanics, chemical kinetics and thermodynamics correspond to kinematics and dynamics, respectively [1]. We show a universal relationship between kinetic fluxes and thermodynamic driving forces in a nonequilibrium chemical reaction network (CRN), which are key concepts in the respective theories. For any stochastic reversible elementary reaction, one-way fluxes in both directions are well defined; they equal to the forward and backward reaction rates. The one-way flux of each reaction cycle is defined through the cycle fluxes in the counting space of the corresponding chemical-master-equation model [14] describing the stochastic kinetics of molecular numbers. Our theory is based on the general mathematical results on cycle fluxes of a Markov process [15,16]: We prove Eq (1) for each reaction cycle by summing over all the corresponding stochastic cycles in the counting space and derive the entropy production rate in terms of the one-way cycle fluxes. We generalize all these results to the most general cases with the presence of multiple material reservoirs
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