Construction of statistical operators for nonequilibrium processes

It is shown that a non-equlibrium statistical operator suitable for describing systems at intervals of time much greater then the “forgetting-time” of the original distribution can be constructed as the invariant part of the quasiequilibrium statistical operator with respect to the evolution of a sistem with a given Hamiltonian $H$. For this form of the nonequilibrium statistical operator, general expressions are obtained that relate the thermodynamic coordinates to the thermodynamic forces as well as a general expression for the entropy prodaction and the generalized kinetic equations that describe the evolution of the thermodinamic variables in time. It is shown that this method of theoretical description of nonequilibrium processes is equivalent to within second-order terms to the method of quasi-integrals of motion proposed by one of the authors [1].