The Gibbs paradox and unidirectional fluxes.

The Gibbs paradox is introduced by means of a particular example: the interdiffusion of two molecular species through a membrane. In the limit when passing from the interdiffusion of two distinct species to that of identical species, the equation for dissipation (or, equivalently, entropy production) fails catastrophically. In the case of an equilibrium system, one finds the paradoxical situation of a zero net flux in conjunction with nonzero dissipation. A general analysis of the problem is given in terms of a metrical theory of irreversible thermodynamics. Its mathematical structure provides a criterion for identity sufficient to resolve the paradox. Metrical aspects of the Principle of Superposition are examined. The paper ends with a discussion of the conceptual and physical difficulties that the Gibbs paradox poses for the idea of unidirectional fluxes. In particular, it is demonstrated that the commonly held notion that net flux is a superposition of an inward and an outward flux violates the Second Law. [ABSTRACT FROM AUTHOR]