THE THERMODYNAMIC DESCRIPTION OF HETEROGENEOUS DISSIPATIVE SYSTEMS BY VARIATIONAL METHODS: IV. CONSEQUENCES OF A SYNTHESIS OF THE ONSAGER AND PRIGOGINE PRINCIPLES

Since Onsager's steady-state dissipation principle and Prigogine's principle of minimum entropy production share a common Euler–Lagrange equation, their configuration spaces may be combined to form a single potential surface. As applied to phase transformations, the entropy production forms a saddle surface in the configuration space of possible stationary states. Those macroscopic variations which involve a change in morphology and a corresponding change in the thermodynamic forces during a spontaneous regression stabilize at a minimum of the entropy production (Prigogine's principle), whereas those microscopic variations, due to fluctuations of the fluxes with fixed forces and fixed morphology, stabilize at a maximum of the entropy production (Onsager's principle). A stable steady state is, therefore, defined by the saddle point.The internal constraints attending stationary phase transformation often exclude the saddle point as a possible state so that unstable configurations are obtained. Dendritic growth of alloy crystals is an example.Some isothermal eutectic or eutectoid reactions may be located at the saddle point. In this case the stabilization of the configuration against microscopic fluctuations requires that the reaction product be in metastable equilibrium. Alteration of the growth conditions may lead to macroscopic instability and a transition to a state lying off the saddle point. These systems evidence their instability by the roughly periodic form of the reaction products.