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- ItemAn entropic gradient structure for Lindblad equations and GENERIC for quantum systems coupled to macroscopic models(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Mittnenzweig, Markus; Mielke, AlexanderWe 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.