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

TL;DR

This paper demonstrates that Lindblad operators satisfying detailed balance can be expressed as gradient systems relative to entropy, and explores thermodynamically consistent quantum-to-macroscopic couplings.

Contribution

It introduces an entropic gradient structure for Lindblad equations and analyzes thermodynamically consistent couplings of quantum systems to macroscopic models.

Findings

Lindblad operators can be written as gradient systems with respect to relative entropy.

Couplings of quantum dots to macroscopic charge carriers are thermodynamically consistent.

Framework unifies quantum dynamics with macroscopic thermodynamic principles.

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