Nonequilibrium thermodynamic formalism of nonlinear chemical reaction systems with Waage–Guldberg’s law of mass action

Abstract

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