An entropic gradient structure for Lindblad equations and GENERIC for quantum systems coupled to macroscopic models
- Mittnenzweig, Markus
- Mielke, Alexander
2010 Mathematics Subject Classification
- 82B10 82C10 47D07 49S05
- Quantum Markov semigroups, open quantum systems, Lindblad operator, detailed-balance condition, relative entropy, Onsager, operators, general equations for non-equilibrium reversible irreversible coupling, GENERIC
We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finite-dimensional Hilbert space satisfying the detailed balance condition with respect to the thermal equilibrium state can be written as a gradient system with respect to the relative entropy. We discuss also thermodynamically consistent couplings to macroscopic systems, either as damped Hamiltonian systems with constant temperature or as GENERIC systems.
- J. Statist. Phys., 167 (2017), pp. 205--233, DOI 10.1007/s10955-017-1756-4 .