Balance between quantum Markov semigroups. (English) Zbl 1392.81167
Summary: 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.
MSC:
| 81S25 | Quantum stochastic calculus |
| 47D07 | Markov semigroups and applications to diffusion processes |
| 46L10 | General theory of von Neumann algebras |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |
| 82C41 | Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics |
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