Derivation of the equations of nonlinear relaxational hydrodynamics by the nonequilibrium statistical operator method.~II

L. A. Pokrovskii

Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 1, pp. 143-156

Résumé

We study irreversible processes in a statistical system of molecules, with internal degrees of freedom, weakly interacting with the external ones. The connected system of kinetic and hydrodynamic equations obtained in the work [1] by the method of the non-equilibrium statistical operator is studied for the nonlinear case. The collision integral and kinetic coefficients are defined by expression of the same type in terms of correlation functions of the quasi-equilibrium ensemble. Using these expressions, the collision integral and the kinetic coefficients are expressed in terms of equilibrium correlation functions referring only to the external degrees of freedom, and in terms of the occupation numbers of the internal degrees of freedom. The collision integral is obtained in a form usual for kinetic theory, but with transition probabilities in the form of spectral densities of the correlation functions. The resulting equations are applied to the problem of sound propagation. The dispersion of the kinetic coefficients and of the heat capacity are studied. For the partial case of a twolevel molecule we find an expression for the so-called “excitation volume of the molecule”. The entropy production is proved to be positive for the system of equations obtained in the case of strong internal non-equilibrium.