An Entropic Gradient Structure for Lindblad Equations and Couplings of Quantum Systems to Macroscopic Models
Abstract
We show that all Lindblad operators (i.e., generators of quantum Markov 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.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- April 2017
- DOI:
- 10.1007/s10955-017-1756-4
- arXiv:
- arXiv:1609.05765
- Bibcode:
- 2017JSP...167..205M
- Keywords:
-
- Quantum Markov semigroups;
- Relative entropy;
- Gradient structure;
- General equations for non-equilibrium reversible irreversible coupling;
- Mathematical Physics
- E-Print:
- J. Stat. Physics 167:2 (2017) 205-233