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

Macroscopic entropy production ${\sigma }^{(tot)}$ in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation and a house-keeping heat: ${\sigma }^{(tot)}={\sigma }^{(fd)}+{\sigma }^{(hk)}$; ${\sigma }^{(fd)}=-\text{rd}A\mathrm{/}\text{rd}t$, where $A$ is a generalized free energy function. This yields a novel nonequilibrium free energy balance equation $\rd A/\rd t=-\sigma^{(tot)}+\sigma^{(hk)}$, which is on a par with celebrated entropy balance equation $\text{rd}S\mathrm{/}\text{rd}t={\sigma }^{(tot)}+{\eta }^{(ex)}$ where ${\eta }^{(ex)}$ is the rate of entropy exchange with the environment.For kinetic systems with complex balance, ${\sigma }^{(fd)}$ and ${\sigma }^{(hk)}$ are the macroscopic limits of stochastic free energy dissipation and house-keeping heat, which are both nonnegative, in the Delbr"uck-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.