Optimal multi-parameter control of trapped active matter

TL;DR

This paper develops a computational framework for optimizing multi-parameter control protocols in active matter systems, achieving near-optimal thermodynamic efficiency and revealing new control strategies beyond single-parameter approaches.

Contribution

It introduces an exact-gradient descent method for deriving optimal multi-parameter control protocols in active matter, including novel strategies like symmetry breaking and non-monotonic controls.

Findings

Smoothed protocols achieve near-optimal efficiency.

Multi-parameter coupling leads to new control strategies.

Naive independent controls are nearly as effective as full optimization.

Abstract

The realization of efficient micro-machines built from active matter requires precise thermodynamic control far from equilibrium. Despite theoretical progress, the focus on single-parameter driving, coupled with strict theoretical assumptions, limits efforts to capture modern multi-parameter control experiments. Here, guided by careful theoretical considerations, we develop a transparent computational framework based on exact-gradient descent via automatic differentiation. We derive optimal protocols for a wide range of multi-parameter problems -- involving trap stiffness, trap center, and particle activity -- to minimize the thermodynamic work or heat. We demonstrate that smoothed, experimentally plausible protocols -- obtained by assigning kinetic costs to the controls -- achieve near-optimal efficiencies comparable to discontinuous ``bang-bang'' solutions. By exploring both open- and closed-loop control, we find the dynamical coupling between parameters leads to genuinely new strategies, including symmetry breaking in optimal activity cycles and non-monotonic trap stiffness controls. Further, we identify regimes where initial measurement and multi-parameter flexibility combine to improve efficiency. Finally, we reveal that the naive simultaneous execution of independently optimized controls incurs only slightly more work than the full multi-parameter solutions. Taken together, our work elucidates the non-equilibrium physics of multi-parameter control and provides robust, scalable strategies for controlling active matter.