Balance between quantum Markov semigroups

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.

v1: 40 pages. v2: Corrections and small additions made, 41 pages

References in corpus (4)

• Joinings of W*-dynamical systems
• Bose-Einstein condensation and condensation of $q$-particles in equilibrium and non equilibrium thermodynamics: a new approach
• Detailed balance and entanglement
• A proposal for the thermodynamics of certain open systems

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