Application of the nonequilibrium statistical operator to the derivation of equations of relaxational nonlinear hydrodynamics (part I)

The method of nonequilibrium statistical operator is applied to investigate irreversible processes in statistical systems whose internal degrees of freedom interact weakly with the external degrees of freedom. It is assumed that the internal degrees of freedom are in a state of strong equilibrium and the external degrees of freedom are approaching local equilibrium expressed by the local temperature and mass velocity. A kinetic equation has been obtained for the internal degrees of freedom; it is interrelated with the system of hydrodynamic equations describing the evolution of the external degrees of freedom. By using correlation functions, relationships have been obtained for the collision integral and for the coefficients connecting both the kinetic and the hydrodynamic equations. Also the linear approximation has been considered for which the equations obtained coincide with those of the phenomenological relaxational hydrodynamics.