An entropic gradient structure for Lindblad equations and couplings of quantum systems to macroscopic models

Understand

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.
• In particular we discuss the coupling of a quantum dot coupled to macroscopic charge carriers.