We give a brief review of applications of the method of the nonequilibrium statistical operator developed by D.N.Zubarev to some problems of nonequilibrium statistical mechanics.

Starting with Dyson equations for the path-ordered Green's function, it is shown that the correlation functions for relativistic electrons (positrons) in a weakly coupled non-equilibrium plasmas can be decomposed into sharply peaked quasiparticle parts and off-shell parts in a rather general form. To leading order in the electromagnetic coupling constant, this decomposition yields the extended quasiparticle approximation for the correlation functions, which can be used for the first principle calculation of the radiation scattering rates in QED plasmas.

The problem of many-particle correlations in different approaches to the quantum kinetic theory is treated on the basis of Zubarev's method of the nonequilibrium statistical operator. It is shown that long-lived correlations can be incorporated through boundary conditions for reduced manyparticle density matrices and the nonequilibrium real-time Green functions. Within the method of Green functions the boundary conditions are conveniently formulated in terms of the "mixed" Green functions defined on a directed contour with the real-time evolution governed by the Hamiltonian of the system and the "imaginary-time" evolution governed by the entropy operator. The perturbation expansion of the mixed Green function is obtained in terms of the interaction part of the Hamiltonian and the correlation part of the entropy operator.

We present a kinetic theory of radiative processes in many-component plasmas with relativistic electrons and nonrelativistic heavy particles. Using the non-equilibrium Green's function technique in many-particle QED, we show that the transverse field correlation functions can be naturally decomposed into sharply peaked (nonLorentzian) parts that describe resonant (propagating) photons and off-shell parts corresponding to virtual photons in the medium. Analogous decompositions are obtained for the longitudinal field correlation functions and the correlation functions of relativistic electrons. We derive a kinetic equation for the resonant photons with a finite spectral width and show that the off-shell parts of the particle and field correlation functions are essential to calculate the local radiating power in plasmas and recover the results of vacuum QED. The plasma effects on radiative processes are discussed.