An Unifying Thermodynamic Framework for Nonlinear Macrokinetics in Reaction-Diffusion Systems

Abstract

Two competing directions in elementary chemical or transport steps are analyzed from the viewpoint of their contribution to the overall rates. Systems with nonlinear transport phenomena and chemical reactions are described by the equations of nonlinear kinetics of the Marcelin-Kohnstamm–de Donder type that contain terms exponential with respect to the Planck potentials and temperature reciprocal. Simultaneously these equations are analytical expressions characterizing the transport of the substance or energy through the energy barrier. They constitute potential representations of a generalized law of mass action that includes the effect of transfer phenomena and external fields. Important are the physical consequences of these kinetics near and far from equilibrium. In these developments nonlinear symmetries and generalized affinity are important. The affinity picture - new for transport phenomena - and the traditional Onsagerian picture are shown to constitute two equivalent representations for kinetics of chemical reactions and transfer processes. Correspondence with the Onsager’s theory is shown closely to the thermodynamic equilibrium. Yet, it can be shown that rates of transport processes and chemical reactions far-from-equilibrium cannot be determined uniquely in terms of their affinities since these rates depend on all state coordinates of the system.