Optimal control strategy for collisional Brownian engines

TL;DR

This paper derives the optimal driving protocol for collisional Brownian engines, revealing a structure of linear force segments and impulsive kicks that maximize power and efficiency while controlling entropy production, providing a benchmark for engine design.

Contribution

It introduces an analytically derived optimal control protocol for collisional Brownian engines, outperforming standard strategies and approaching near-unity efficiency at maximum power.

Findings

Optimal protocol involves linear forces and impulsive velocity reversals.

Achieves higher power and efficiency than traditional driving strategies.

Maintains high performance even with realistic force smoothing.

Abstract

Collisional Brownian engines have recently gained attention as alternatives to conventional nanoscale engines. However, a comprehensive optimization of their performance, which could serve as a benchmark for future engine designs, is still lacking. In this work, we address this gap by deriving and analyzing the optimal driving protocol for a collisional Brownian engine. By maximizing the average output work, we show that the optimal protocol consists of linear force segments separated by impulsive delta-like kicks that instantaneously reverse the particle's velocity. This structure enforces constant velocity within each stroke, enabling fully analytical expressions for optimal output power, efficiency, and entropy production. We demonstrate that the optimal protocol significantly outperforms standard strategies (such as constant, linear, or periodic drivings) achieving higher performance while keeping entropy production under control. Remarkably, when evaluated using realistic experimental parameters, the efficiency approaches near-unity at the power optimum, with entropy production remaining well controlled, a striking feature of the optimal protocol. To analyze a more realistic scenario, we examine the impact of smoothing the delta-like forces by introducing a finite duration and find that, although this reduces efficiency and increases entropy production, the optimal protocol still delivers high power output in a robust manner. Altogether, our results provide a theoretical benchmark for finite-time thermodynamic optimization of Brownian engines under time-periodic drivings.