Nonequilibrium Thermodynamic Formalism of Nonlinear Chemical Reaction Systems with Waage-Guldberg's Law of Mass Action

Abstract

Macroscopic entropy production $\ddot{I}{ƒ}^{(tot)}$ in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation and a house-keeping heat: $\ddot{I}{ƒ}^{(tot)}=\ddot{I}{ƒ}^{(fd)}+\ddot{I}{ƒ}^{(hk)}$; $σ^{(fd)}=-\rd A/\rd t$, where $A$ is a generalized free energy function. This yields a novel nonequilibrium free energy balance equation $\rd A/\rd t=-σ^{(tot)}+σ^{(hk)}$, which is on a par with celebrated entropy balance equation $\rd S/\rd t=σ^{(tot)}+η^{(ex)}$ where $\hat{I}{\cdot }^{(ex)}$ is the rate of entropy exchange with the environment.For kinetic systems with complex balance, $\ddot{I}{ƒ}^{(fd)}$ and $\ddot{I}{ƒ}^{(hk)}$ are the macroscopic limits of stochastic free energy dissipation and house-keeping heat, which are both nonnegative, in the Delbrück-Gillespie description of the stochastic chemical kinetics.Therefore, we show that a full kinetic and thermodynamic theory of chemical reaction systems that transcends mesoscopic and macroscopic levels emerges.

24 pages