New Stability Criteria for Reaction-diffusion

A new variational approach to irreversible thermodynamics has been developed leading to lagrangian equations of evolution. The essential results have been presented recently in the form of a short monograph [l]. Its foundation rests on a fundamental principle of virtual dissipation. Our purpose here is to derive new stability criteria for a steady state evolution based on lagrangian equations in the context of general reaction-diffusion. As a preliminary, the concepts of local energy and entropy per unit volume under irreversible evolution are given a precise definition and a new expression is also developed for the affinity which embodies chemical kinetics. A special derivation of the variational and the lagrangian equations is presented in the particular context of reaction-diffusion as well as a general expression for thermomolecular dissipation which is invariant under translation. A new stability criterion is obtained which does not require “local equilibrium” and distinguishes between oscillatory and non-oscillatory stability. The lagrangian equations also lead directly to a stability criterion analogous to that proposed by Glansdorff and Prigogine [2] providing at the same time a precise definition of an associated condition of “ local equilibrium”. 2. Outline of a new thermochemistry