This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Mittnenzweig, MarkusMielke, Alexander2016-12-172019-06-2820162198-5855https://doi.org/10.34657/1971https://oa.tib.eu/renate/handle/123456789/1688We 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.application/pdfeng510Quantum Markov semigroupsopen quantum systemsLindblad operatordetailedbalance condition. relative entropyOnsager operatorsgeneral equations for non-equilibrium reversible irreversible couplingGENERICReport