Markov Form of the Method of Nonequilibrium Statistical Operator

TL;DR

This paper derives a Markov form of the nonequilibrium statistical operator using projection operators, enabling simplified kinetic equations without memory effects for practical applications.

Contribution

It introduces an explicit non-Markov form of the NSO and demonstrates its equivalence to other methods, along with an exact transformation to a Markov form for arbitrary time dependence.

Findings

Derived a non-Markov form of NSO using the Kawasaki-Gunton projection operator.

Proved the equivalence of the non-Markov form to boundary condition methods.

Obtained generalized kinetic equations without memory effects.

Abstract

The general principles of the choice of the reduced description parameters of nonequilibrium states γα(t) and the construction of the nonequilibrium statistical operator (NSO) ρ(t) are discussed. On the basis of Kavasaki - Gunton projection operator an explicit non-Markov form of NSO with respect to parameters is obtained and the equivalence of the method to the other methods using boundary conditions for ρ(t) or "mixing" operator is shown. An exact NSO transformation to γα(t) Markov form with respect to γα(t) at arbitrary dependence of Vt perturbation on time is made. The generalized kinetic equations not containing the memory with respect to γα(t) are obtained being convenient for practical application.