On how nanomechanical systems can minimize dissipation

TL;DR

This paper explores how nanomechanical systems can be optimally controlled to minimize energy dissipation, linking optimal control, mass transport, and kinetic equations to improve nanoscale energy efficiency.

Contribution

It introduces a natural derivation of optimal control equations considering energy costs, connecting them to mass transport and kinetic equations for nanosystems.

Findings

Optimal control equations incorporate energy costs for potential manipulation.

In the negligible energy cost limit, solutions relate to optimal mass transport.

Hierarchies of kinetic equations are equivalent to the derived control equations.

Abstract

Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. In this letter we focus on mechanical systems controlled by smoothly varying potential forces. We show that optimal control equations come about in a natural way if the energy cost to manipulate the potential is taken into account. When such cost becomes negligible, the optimal control strategy can be constructed by transparent geometrical methods and recovers the solution of optimal mass transport equations in the overdamped limit. Our equations are equivalent to hierarchies of kinetic equations of a form well-known in the theory of dilute gases. From our results, optimal strategies for energy efficient nanosystems may be devised