  Nonequilibrium statistical physics is concerned with a fundamental problem in
physics, the phenomenon of irreversibility, which is not rigorously solved yet.
Different approaches to the statistical mechanics of nonequilibrium processes
are based on empirical assumptions but a rigorous, first principle theory is
missing. An important contribution to describe irreversible behavior starting
from reversible Hamiltonian dynamics was given by Zubarev who invented the
method of the nonequilibrium statistical operator (NSO). We discuss this
approach, in particular the extended von Neumann equation and the entropy
concept. The method of NSO proved to be a general and universal approach to
different nonequilibrium phenomena. Typical applications are the quantum master
equation, kinetic theory, and linear response theory which are outlined and
illustrated solving standard examples for reaction and transport processes.
Some open questions are emphasized.
