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The method of the nonequilibrium statistical operator developed by D. N.Zubarev is employed to analyse and derive generalized transport and kineticequations. The degrees of freedom in solids can often be represented as a fewinteracting subsystems (electrons, spins, phonons, nuclear spins, etc.).Perturbation of one subsystem may produce a nonequilibrium state which is thenrelaxed to an equilibrium state due to the interaction between particles orwith a thermal bath. The generalized kinetic equations were derived for asystem weakly coupled to a thermal bath to elucidate the nature of transportand relaxation processes. It was shown that the "collision term" had the samefunctional form as for the generalized kinetic equations for the system withsmall interactions among particles. The applicability of the general formalismto physically relevant situations is investigated. It is shown that some knowngeneralized kinetic equations (e.g. kinetic equation for magnons, Peierlsequation for phonons) naturally emerges within the NSO formalism. Therelaxation of a small dynamic subsystem in contact with a thermal bath isconsidered on the basis of the derived equations. The Schrodinger-type equationfor the average amplitude describing the energy shift and damping of a particlein a thermal bath and the coupled kinetic equation describing the dynamic andstatistical aspects of the motion are derived and analysed. The equationsderived can help in the understanding of the origin of irreversible behavior inquantum phenomena.Comment: 21 pages, Revte

GENERALIZED KINETIC AND EVOLUTION EQUATIONS IN THE APPROACH OF THE NONEQUILIBRIUM STATISTICAL OPERATOR