Non-Markovian feedback control and acausality: an experimental study

TL;DR

This experimental study investigates how non-Markovian, acausal feedback control affects fluctuation relations in a nanoparticle system, revealing signatures of acausality in nonequilibrium thermodynamic properties.

Contribution

It demonstrates experimentally that acausal, time-delayed feedback modifies fluctuation relations, highlighting the impact of non-Markovian effects on nonequilibrium thermodynamics.

Findings

Acausality manifests in fluctuation relations for the system.

Long-time steady-state fluctuation relations reveal signatures of acausality.

Time-reversed dynamics are not physically realizable but influence the observed properties.

Abstract

Causality is an important assumption underlying nonequilibrium generalizations of the second law of thermodynamics known as fluctuation relations. We here experimentally study the nonequilibrium statistical properties of the work and of the entropy production for an optically trapped, underdamped nanoparticle continuously subjected to a time-delayed feedback control. Whereas the non-Markovian feedback depends on the past position of the particle for a forward trajectory, it depends on its future position for a time-reversed path, and is therefore acausal. In the steady-state regime, we show that the corresponding fluctuation relations in the long-time limit exhibit a clear signature of this acausality, even though the time-reversed dynamics is not physically realizable.