# Thermodynamics of continuous non-Markovian feedback control

## TL;DR

This paper experimentally explores the thermodynamics of continuous, non-Markovian feedback control with time delays, testing a generalized second law and examining feedback cooling limits in an optically levitated microparticle system.

## Contribution

It provides the first experimental validation of a generalized second law for non-Markovian feedback and analyzes the effects of time delays on feedback cooling.

## Key findings

- Generalized second law bounds energy extraction in delayed feedback.
- Feedback cooling breaks down at large time delays.
- Experimental validation of thermodynamic principles in non-Markovian control.

## Abstract

Feedback control mechanisms are ubiquitous in science and technology, and play an essential role in regulating physical, biological and engineering systems. The standard second law of thermodynamics does not hold in the presence of measurement and feedback. Most studies so far have extended the second law for discrete, Markovian feedback protocols; however, non-Markovian feedback is omnipresent in processes where the control signal is applied with a non-negligible delay. Here, we experimentally investigate the thermodynamics of continuous, time-delayed feedback control using the motion of an optically levitated, underdamped microparticle. We test the validity of a generalized second law which bounds the energy extracted from the system and study the breakdown of feedback cooling for very large time delays.