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| Title: | An entropic gradient structure for Lindblad equations and GENERIC for quantum systems coupled to macroscopic models |
| Authors: | Mittnenzweig, Markus; Mielke, Alexander |
| Issue Date: | 2016 |
| Published in: | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2320, ISSN 2198-5855 |
| Publisher: | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik |
| Abstract: | 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. |
| Keywords: | Quantum Markov semigroups; open quantum systems; Lindblad operator; detailedbalance condition. relative entropy; Onsager operators; general equations for non-equilibrium reversible irreversible coupling; GENERIC |
| DDC: | 510 |
| License: | 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. |
| Appears in Collections: | Mathematik |
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