# Non-Equilibrium Statistical Operator

## TL;DR

The paper reviews the nonequilibrium statistical operator method, a rigorous approach to irreversibility in statistical physics, highlighting its applications and open questions in describing irreversible phenomena from reversible dynamics.

## Contribution

It discusses the Zubarev nonequilibrium statistical operator method, emphasizing its generality and applications in quantum and kinetic theories, and addresses open problems in the field.

## Key findings

- NSO provides a universal framework for nonequilibrium phenomena.
- Applications include quantum master equations and kinetic theory.
- The approach offers insights into irreversibility from reversible dynamics.

## Abstract

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.