Extracting work from a single reservoir in the non-Markovian underdamped regime

TL;DR

This paper derives optimal finite-time work protocols for a colloidal particle in a non-Markovian underdamped regime, revealing how measurements and forcing conditions influence work extraction efficiency.

Contribution

It introduces the first derivation of optimal work protocols in the non-Markovian underdamped regime, including effects of measurements and forcing conditions.

Findings

Protocols without measurement decrease work linearly with forced start-stop conditions.

Protocols with measurements can outperform non-measurement protocols at short times.

Velocity measurements extract more work than position measurements.

Abstract

We derive optimal-work finite time protocols for a colloidal particle in a Gaussian well in the general non-Markovian underdamped regime in contact with a single reservoir. Optimal work protocols with and without measurements of position and velocity are shown to be linear in time. In order to treat the underdamped regime one must address forcing the particle at the start and at the end of a protocol, conditions which dominate the short time behaviour of the colloidal particle. We find that for protocols without measurement the least work by an external agent decreases linearly for forced start-stop conditions while those only forced at starting conditions are quadratic (slower) at short times, while both decrease asymptotically to zero for quais-static processes. When measurements are performed protocols with start-end forcing are still more efficient at short times but can be overtaken by start-only protocols at a threshold time. Measurement protocols derive work from the reservoir but always below the predicted by the Sagawa's generalization of the second law. Velocity measurement protocols are more efficient in deriving work than position measurements.