Information-theoretic stability and evolution criteria in irreversible thermodynamics

Abstract

Generalized information gains are used to derive stability conditions, for steady states, periodic orbits and invariant sets, and general evolution criteria, both global and local with respect to the time variable, in irreversible thermodynamics. Meixner's passivity condition and the Glansdorff-Prigogine stability and evolution criteria are found to be special cases thereof. The information gain quantities include Kullback's three kinds of divergences, the first two of which are dual to each other and yield criteria which are symmetric in the average densities of the system's extensive variables and the conjugate parameters, but which are nonsymmetric in the irreversible fluxes and forces, while the third one does not involve the entropy function of the system. Furthermore, Renyi's information gain of orderα and Csiszar'sf-divergence are treated. The latter is used to construct a most general information gain quantity as a Liapunov function and evolution criterion, which, however, for local stability and evolution conditions is still equivalent to the use of the second-order variation of the entropy.