Nonequilibrium Statistical Mechanics of a Multicomponent Fluid

A general theory of linear nonequilibrium statistical mechanics proposed by Baur, Jordan, Jordan, and Mayer is applied to a model system: the multicomponent, chemically nonreactive fluid. This theory centers on the determination of a set of conjugate intensive and extensive thermodynamic variables such that a displacement in any one of these variables relaxes to equilibrium without exciting any of the others. The matrix equations which govern the solution of this problem are determined both via thermodynamics and via statistical mechanics. A complete solution is given for one- and two-component systems and that displacement function corresponding to a sound wave determined for the n-component system. In order for thermodynamics and statistical mechanics to correspond, the Onsager matrix is identified with its microscopic analog. In this way, expressions for transport coefficients are found which are equivalent to those found using more conventional methods. Applications to the problem of light scattering are discussed and general formulas for the ratio of the intensities of the frequency shifted line to the nonfrequency shifted line are determined for multicomponent systems. Possible methods of direct observation of these independently decaying thermodynamic variables (other than the sound wave) are considered.