The variational principles of Onsager and Prigogine in membrane transport

Abstract

Whilst Onsager's principle of least dissipation of energy and Prigogine's principle of minimal entropy production both refer to the extremum value of a space integral, Hamilton's principle refers to a definite time integral. With the help of cyclic variables, Onsager's theorem can be transformed into a space–time variational problem. Using a method of Hilbert, a field of extremals can be obtained, composed of potential gradients µ_i and the coordinated geodesic slopes j_i. Only these field quantities furnish the validity of linear thermodynamics; the choice of arbitrary fluxes and forces, however, requires the introduction of excess terms resulting from a theorem of Weierstrass.