Quantum thermodynamics of continuous feedback control

TL;DR

This paper develops a formalism for applying thermodynamic laws to open quantum systems under continuous measurement and feedback, providing new insights into energy flows and irreversibility in quantum control scenarios.

Contribution

It introduces a novel framework for quantum thermodynamics with continuous feedback, including derivations of work, heat, and entropy production expressions.

Findings

Derived thermodynamic quantities for quantum feedback systems.

Analyzed a continuous measurement-driven Szilard engine.

Explored irreversibility and energetics in quantum feedback control.

Abstract

The laws of thermodynamics are a cornerstone for describing nanoscale and open quantum systems. However, formulating these laws for systems under continuous feedback control and under experimentally relevant conditions is challenging. In this work, we lay out a formalism for the laws of thermodynamics in an open quantum system under continuous measurement and feedback described by a Quantum Fokker Planck Master Equation. We derive expressions for work, heat, and measurement-induced energy changes, and we investigate entropy production and fluctuation theorems. We illustrate our results with a continuous version of a measurement-driven Szilard engine, as well as a work extraction scheme in a two-level system under bang-bang control. Our results provide insights into the energetics as well as the irreversibility of classical and quantum systems under continuous feedback control.