Onsager reciprocity as a consequence of Maxwell reciprocity for “equidiffuse” fluids

Abstract

Linear irreversible thermodynamics (LIT) principles are used to show, in the hypothetical “equidiffuse” case where all of the various phenomenological diffusion coefficients appearing in the linear near-equilibrium constitutive laws governing the diffuse transport of energy, multicomponent species, entropy, and volume (although not necessarily including momentum) are taken to be equal, that the Onsager reciprocal relations pertinent to nonequilibrium thermodynamics follow automatically from Maxwell’s reciprocal relations governing equilibrium thermodynamics. As such, this constitutes a purely macroscopic proof of Onsager reciprocity, the first of its kind. Although the equality of diffusion coefficients required in the equidiffuse limiting case does not represent a realistic possibility in the case of most mixtures, its adoption as a foil in uniting reversible and irreversible thermodynamics neither violates nor conflicts with any known physical law. Indeed, in some idealized sense such equality represents a perfection of the well-known analogy between these distinct physical transport phenomena. Moreover, as shown for mixtures of chemically similar dilute gases of comparable molecular weights (e.g., consecutive members of a homologous series) the equidiffuse assumption is generally quite good. As a bonus, our analysis — by virtue of its accord with all known precepts of macroscopic physics — constitutes a satisfactory resolution of the long-standing criticism of Coleman and Truesdell [B.D. Coleman, C. Truesdell, On the reciprocal relations of Onsager, J. Chem. Phys. 33 (1960) 28–31] centered on the possibility that Onsager symmetry might be nothing more than a tautology (derisively referred to in the literature as “Onsagerism”).