  One of the fundamental problems in physics which are not rigorously solved
yet is the statistical mechanics of nonequilibrium processes. An important
contribution to describe irreversible behavior starting from reversible
Hamiltonian dynamics was given by D. N. Zubarev who invented the method of the
nonequilibrium statistical operator (NSO). We discuss this approach, in
particular the extended von Neumann equation, and consider as example the
electrical conductivity of a charged particle system. The selection of the set
of relevant observables is considered. The relation between kinetic theory and
linear response theory is shown. Using thermodynamic Green functions, a
systematic treatment of correlation functions is given, but convergence has to
be investigated. Different expressions for the conductivity are compared, and
open questions are identified.
