  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:
$\sigma^{(tot)}=\sigma^{(fd)}+\sigma^{(hk)}$; $\sigma^{(fd)}=-\rd A/\rd t$,
where $A$ is a generalized free energy function. This yields a novel
nonequilibrium free energy balance equation $\rd A/\rd
t=-\sigma^{(tot)}+\sigma^{(hk)}$, which is on a par with celebrated entropy
balance equation $\rd S/\rd t=\sigma^{(tot)}+\eta^{(ex)}$ 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.
