Stability and relative stability in reactive systems far from equilibrium. I. Thermodynamic analysis

Abstract

We present in this article an analysis of the stability and relative stability of multiple stationary states in chemical systems driven far from equilibrium. Given the macroscopic kinetic (nonlinear) equations of motion, we postulate that there exists an entropy state function which is maximum for the (time-dependent) solutions (concentrations of chemical species as a function of time) of the kinetic equations. We derive thermodynamic equations of motion for multivariable systems which follow from a thermodynamic variational principle for the power dissipation and are consistent with the kinetic equations. From the thermodynamic equations of motion we obtain conditions for stability, marginal stability, and relative stability of stationary states. The point of coexistence of stationary states, being a special case of relative stability, is identified. We discuss examples of one and two variable systems. The thermodynamic analysis for a one-variable system agrees with a stochastic solution, and with a kinetic analysis presented in the next article.