The principle of increasing mixing character and some of its consequences

Abstract

The “Principle of Increasing Mixing Character”, previously postulated by one of us (and derived for the case of an ensemble of isolated systems obeying a “master equation”) as a stronger version of the second law of thermodynamics, is re-derived using von Neumann's density matrix formulation of statistical mechanics. To make the principle more convenient for applications, it is reformulated in terms of “Mixing Homomorphic Functions”, a set of state functions all of which must increase in an allowed irreversible process in an-isolated system. The entropy is one such function, but no one function, and no finite set of functions, suffices to determine the increase of mixing character. The principle is extended to the case of a system which is not isolated, but in contact with a heat bath, for which it takes a form which we name the “Principle of Decreasing Mixing Distance” from the equilibrium distribution. As examples, applications are made to two simple cases: diffusion in an ideal solution, and chemical reactions in ideal gas mixtures.