Properties of the phenomenological coefficients in the cases of dependent fluxes and/or dependent forces. A unified theorem

Abstract

Properties of the phenomenological coefficients (PC) of irreversible thermodynamics in the case of linear homogeneous relationships between (a) the fluxes only, (b) the forces only and (c) both the fluxes and the forces are analysed, with the fundamental argument that the dissipation function, given in the bilinear form as a sum of q products of pairs of conjugate fluxes and forces, is invariant under the elimination of any pair of fluxes and forces taken arbitrarily as dependent quantities. It is shown that in all cases the PC are still uniquely defined, the Onsager reciprocal relations remain valid and there exist 2q–1 linear relations among the q² PC. The q-fold arbitrariness in the PC found by De Groot and Mazur in the case of dependent fluxes and forces is shown to be only apparent, as it is compensated by another arbitrariness of the same order implied in the choice of the dependent quantities.