Minimal entropy production in systems under constraint

Abstract

Applying a variational method given by Hilbert to a theorem of Onsager an expression for the minimal entropy production in systems under constraint can be obtained.

Application is made to transport processes in membranes where free ions (Donnan ions) as well as ions under constraint (counter ions) are present. Whilst the entropy production of a free particle is given by the product of the flux and its coordinated chemical potential, the latter quantity is reduced for an ion under constraint by the streaming potential and, in the case of the solvent under constraint, by the electroosmotic pressure.