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One of the fundamental problems in physics which are not rigorously solvedyet is the statistical mechanics of nonequilibrium processes. An importantcontribution to describe irreversible behavior starting from reversibleHamiltonian dynamics was given by D. N. Zubarev who invented the method of thenonequilibrium statistical operator (NSO). We discuss this approach, inparticular the extended von Neumann equation, and consider as example theelectrical conductivity of a charged particle system. The selection of the setof relevant observables is considered. The relation between kinetic theory andlinear response theory is shown. Using thermodynamic Green functions, asystematic treatment of correlation functions is given, but convergence has tobe investigated. Different expressions for the conductivity are compared, andopen questions are identified.

Electrical conductivity of charged particle systems and the Zubarev NSO method