Universal symmetry of optimal control at the microscale

TL;DR

This paper reveals a universal time-reversal symmetry in optimal control protocols for microscale transport processes across various media, providing a fundamental criterion to improve energy efficiency and optimization strategies.

Contribution

It demonstrates that optimal control protocols at the microscale universally obey a time-reversal symmetry, even in complex, non-thermal systems, and shows how this insight enhances optimization algorithms.

Findings

Optimal protocols exhibit time-reversal symmetry in viscous and viscoelastic media.

The symmetry applies universally across active, granular, and correlated systems.

Machine learning algorithms benefit from exploiting this symmetry for better optimization.

Abstract

Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here we investigate experimentally and theoretically the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimal. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms.