Energy-Efficient Control of Interacting Microscopic Systems: When Longer Paths Save Energy

TL;DR

This paper explores how controlling interacting microscopic systems, like colloidal particles, can be optimized for energy efficiency, revealing that straight-line paths are optimal in low-noise conditions, while curved paths can be more efficient with hydrodynamic interactions.

Contribution

It provides a theoretical framework for optimal control of interacting particles and experimentally demonstrates energy savings through curved trajectories in hydrodynamic coupling.

Findings

Optimal trajectories are linear in low-noise, conservative systems.

Curved paths can reduce energy costs in hydrodynamic interactions.

Conservative interactions do not alter the geometry of optimal paths.

Abstract

We experimentally and theoretically study the thermodynamically optimal control of interacting multiple-particle systems, focusing on collections of colloidal particles individually confined in optical traps. We investigate protocols that transport the system between prescribed trap configurations within a fixed time in the most energy efficient way. For Markovian systems with conservative pairwise interactions, we establish a general result in the low-noise limit: optimal particle trajectories are linear in space and time, corresponding to steady straight-line motion, irrespective of the specific interaction potential, even for nonlinear forces. Thus, conservative interactions do not modify the geometry of the optimal paths. This property breaks down in the presence of strong noise or nonconservative interactions. For the paradigmatic case of hydrodynamic coupling, we demonstrate experimentally that optimal control can involve curved trajectories that significantly reduce the energetic cost by exploiting collectively generated fluid flows. The emergence of curved paths as optimal solutions highlights a fundamental distinction between non-interacting and interacting systems and reveals a cooperative mechanism for energy-efficient control.