Optimal Control of Overdamped Systems

TL;DR

This paper derives a simple formula for optimizing energy dissipation in small-scale systems driven out of equilibrium, applying it to models of information erasure and molecular motors to find minimal dissipation protocols.

Contribution

It introduces a compact expression for the inverse diffusion tensor based solely on equilibrium data, applicable to a broad class of potentials, enabling efficient optimization of nonequilibrium processes.

Findings

Minimal dissipation inversely proportional to protocol duration.

Derived inverse diffusion tensor depends only on equilibrium information.

Optimized protocols reduce energy loss in model systems.

Abstract

Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles underlying biological processes at the molecular level. Recent work has demonstrated that when a thermodynamic system is driven away from equilibrium then the space of controllable parameters has a Riemannian geometry induced by a generalized inverse diffusion tensor. We derive a simple, compact expression for the inverse diffusion tensor that depends solely on equilibrium information for a broad class of potentials. We use this formula to compute the minimal dissipation for two model systems relevant to small-scale information processing and biological molecular motors. In the first model, we optimally erase a single classical bit of information modelled by an overdamped particle in a smooth double-well potential. In the second model, we find the minimal dissipation of a simple molecular motor model coupled to an optical trap. In both models, we find that the minimal dissipation for the optimal protocol is inversely proportional to protocol duration, as expected, though the dissipation for the erasure model takes a different form than what we found previously for a similar system.