Optimal control with a strong harmonic trap

TL;DR

This paper develops a method for designing optimal control protocols in systems with quadratic traps, minimizing dissipation in molecular manipulations and simulations, applicable across various durations and system types.

Contribution

It introduces a new, easily solvable approach for optimal control in multidimensional quadratic trapping potentials that does not depend on system speed limits.

Findings

Protocols effectively minimize dissipation in molecular systems

Applicable to a wide range of system durations and strengths

Demonstrated on a rotary motor model

Abstract

Quadratic trapping potentials are widely used to experimentally probe biopolymers and molecular machines and drive transitions in steered molecular-dynamics simulations. Approximating energy landscapes as locally quadratic, we design multidimensional trapping protocols that minimize dissipation. The designed protocols are easily solvable and applicable to a wide range of systems. The approximation does not rely on either fast or slow limits and is valid for any duration provided the trapping potential is sufficiently strong. We demonstrate the utility of the designed protocols with a simple model of a periodically driven rotary motor. Our results elucidate principles of effective single-molecule manipulation and efficient nonequilibrium free-energy estimation.