Finite-Time Optimal Control by Noisy Traps

TL;DR

This paper investigates how finite-time optimal control protocols emerge in passive systems when the controller is dissipative and driven out of equilibrium, especially under stochastic fluctuations that break detailed balance.

Contribution

It reveals a transition from infinite to finite optimal protocol durations driven by nonequilibrium fluctuations in a controlled Brownian system.

Findings

Optimal protocols become finite-time when controller fluctuations break detailed balance.

A critical fluctuation strength marks the transition to zero-duration protocols.

Imposing endpoint constraints prevents the transition, maintaining finite protocols.

Abstract

The optimal control of passive systems in equilibrium typically favours quasistatic (infinite-time) protocols. We show that a breakdown of quasistatic optimality occurs when the controller itself is dissipative. Concretely, we study a Brownian particle confined by a harmonic trap with stochastically fluctuating stiffness, driven by an external protocol. When these fluctuations violate detailed balance, the probe-controller coupling continuously exchanges work with the system, altering the optimisation landscape. In this regime, optimal protocols are characterised by a finite duration which vanishes above a critical fluctuation strength. This transition can be directly observed in a short-time expansion of the mean work functional. When imposing an endpoint constraint, the transition to zero duration disappears and finite duration protocols remain optimal for all values of the controller fluctuations. These results demonstrate that finite-time optimality can emerge in passive systems under nonequilibrium control.