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 oneway 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.

Information Geometric Inequalities of Chemical Thermodynamics

“…Although analogy between stochastic thermodynamics and chemical thermodynamics has been studied [9,10,12,[50][51][52][53][54][55][56][57][58], connections between chemical thermodynamics and information theory are still vague because rate equations which govern chemical reactions are based on unnormalized concentration distributions rather than probability distributions. Nevertheless, a few researches have been conducted from the perspective of a connection between chemical thermodynamics and information theory [10,59], focusing on the fact that the pseudo-Helmholtz function has a similar form to the Kullback-Leibler divergence, which plays a fundamental role in information theory.…”