Quantum Theory of Irreversibility

TL;DR

This paper develops a quantum framework for nonequilibrium entropy and irreversibility, extending classical concepts to quantum many-body systems and deriving a quantum Boltzmann equation.

Contribution

It introduces a generalized quantum entropy based on the BBGKY hierarchy and derives a quantum Boltzmann equation from microscopic principles.

Findings

Entropy production is non-negative in isolated quantum systems.

A quantum master matrix and transition superoperator are formulated.

The quantum Boltzmann equation is derived from first principles.

Abstract

A generalization of the Gibbs-von Neumann relative entropy is proposed based on the quantum BBGKY [Bogolyubov-Born-Green-Kirkwood-Yvon] hierarchy as the nonequilibrium entropy for an N-body system. By using a generalization of the Liouville-von Neumann equation describing the evolution of a density super- operator, it is demonstrated that the entropy production for an isolated system is non-negative, which provides an arrow of time. Moreover, following the procedure of non-equilibrium thermodynamics a master matrix is introduced for which a mi- croscopic expression is obtained. Then, the quantum Boltzmann equation is derived in terms of a transition superoperator related to that master matrix.