WIAS Preprint No. 2320, (2016)

An entropic gradient structure for Lindblad equations and GENERIC for quantum systems coupled to macroscopic models



Authors

  • Mittnenzweig, Markus
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 82B10 82C10 47D07 49S05

Keywords

  • Quantum Markov semigroups, open quantum systems, Lindblad operator, detailed-balance condition, relative entropy, Onsager, operators, general equations for non-equilibrium reversible irreversible coupling, GENERIC

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.

Appeared in

Download Documents

  • PDF Version of October 21, 2016 (483 kByte)
  • PDF Version of March 01, 2017 (386 kByte)