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, in particular, the extended von Neumann equation and the entropy concept in this approach. 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.
Part of the book: Non-Equilibrium Particle Dynamics