From a least action principle to mass action law and extended affinity

Abstract

Basic nonlinear laws that govern nonlinear chemical kinetics and diffusion in a far-from-equilibrium nonstationary regime are derived from an action functional of Hamilton's type. The functional operates with the difference between the kinetic and static free energies F kin and F stat and contains an exponential dissipative term that takes into account thermodynamic irreversibility. Unsteady-state generalization of Guldberg and Waage's kinetic law and Fick's law of diffusion is found which goes over into the classical laws at the steady state when local nonequilibrium effects are ignored. Nonlinear irreversible thermodynamics of chemically reacting systems are investigated. An extended chemical affinity à j is obtained which depends not only on the usual equilibrium quantities T and C but also on nonequilibrium variables such as diffusive fluxes J i and reaction rates r j . It is shown that for a far-from-equilibrium and highly nonstationary regime the thermodynamic force for the j-th chemical reaction, X j ch, is the sum of à j and the time derivative of the so-called “reaction momentum” ∂ F kin/∂ r j , and hence the reaction rate r j depends not only on the current state but also on the past history of the reaction.