Optimal Control of Rotary Motors

TL;DR

This paper develops optimal driving protocols for a simplified rotary motor model, minimizing energy dissipation near equilibrium by leveraging thermal fluctuations and system-specific friction characteristics.

Contribution

It introduces a new model with a periodic friction coefficient and derives protocols that outperform naive approaches in minimizing dissipation.

Findings

Protocols slow down near energy barriers to reduce work input.

Fast protocols can effectively 'lap' the system, exploiting thermal fluctuations.

Designed protocols outperform naive driving strategies.

Abstract

Single-molecule experiments have found near-perfect thermodynamic efficiency in the rotary motor F1-ATP synthase. To help elucidate the principles underlying nonequilibrium energetic efficiency in such stochastic machines, we investigate driving protocols that minimize dissipation near equilibrium in a simple model rotary mechanochemical motor, as determined by a generalized friction coefficient. Our simple model has a periodic friction coefficient that peaks near system energy barriers. This implies a minimum-dissipation protocol that proceeds rapidly when the system is overwhelmingly in a single macrostate, but slows significantly near energy barriers, thereby harnessing thermal fluctuations to kick the system over energy barriers with minimal work input. This model also manifests a phenomenon not seen in otherwise similar non-periodic systems: sufficiently fast protocols can effectively lap the system. While this leads to a non-trivial tradeoff between accuracy of driving and energetic cost, we find that our designed protocols out-perform naive protocols.