Balance between quantum Markov semigroups

TL;DR

This paper introduces and explores the concept of balance between quantum Markov semigroups, extending quantum detailed balance, with implications for non-equilibrium statistical mechanics and quantum correlations.

Contribution

It defines a new notion of balance using correlated states, connecting it to Connes correspondences and expanding the theoretical framework of quantum Markov processes.

Findings

Balance is characterized via correlated states and entanglement.

Basic properties of quantum balance are established.

Potential applications to non-equilibrium statistical mechanics are discussed.

Abstract

The concept of balance between two state preserving quantum Markov semigroups on von Neumann algebras is introduced and studied as an extension of conditions appearing in the theory of quantum detailed balance. This is partly motivated by the theory of joinings. Balance is defined in terms of certain correlated states (couplings), with entangled states as a specific case. Basic properties of balance are derived and the connection to correspondences in the sense of Connes is discussed. Some applications and possible applications, including to non-equilibrium statistical mechanics, are briefly explored.