Variational principle for entropy in electrochemical transport phenomena

Transport of energy, matter and electric charge is analyzed in the framework of a quasilinear variational formalism. A new extremum principle extending that of Onsager to a nonstationary quasilinear regime is applied to electrochemical transport. The principle is set in physical space-time rather than in three-dimensional space and, as such, it substantiates the role of the entropy rather than the entropy production. For the prescribed state and/or fluxes at the system boundary the principle implies a least possible growth of entropy under the constraints imposed by conservation laws, which proves that the entropy plays a role in thermodynamics similar to that of action in mechanics. One can use the principle to derive nontruncated sets of the phenomenological equations, equations of change and bulk overvoltage properties in complex systems. The paper prepares a background to dynamical formulations for electrochemical processes. The nonequilibrium temperatures and chemical potentials are interpreted in terms of the Lagrangian multipliers of the variational principle for the entropy. These quantities converge to the classical thermodynamic intensities when the local equilibrium is attained in the system. (C) 1996 Elsevier Science Ltd