Optimal Control of a Mesoscopic Information Engine

TL;DR

This paper analytically solves the optimal control problem for a mesoscopic information engine driven by an overdamped particle, optimizing measurement and control protocols within a POMDP framework to maximize net gain.

Contribution

It introduces a unified LQG-based approach to derive optimal measurement and control strategies for mesoscopic engines, extending existing protocols to more general settings.

Findings

Derived the optimal feedback control law for trap placement.

Evaluated the optimal measurement protocol for binary sensors.

Identified the phenomenon of deadline-induced blindness.

Abstract

We analytically solve the finite-time control problem of driving an overdamped particle via an optical trap under costly measurement. By formulating this mesoscopic information engine within the Partially Observable Markov Decision Process (POMDP) framework, we demonstrate that the underlying Linear-Quadratic-Gaussian (LQG) dynamics decouple the optimal measurement and driving protocols. We derive the optimal feedback control law for the trap placement, which recovers the discontinuous Schmiedl-Seifert driving protocol in the open-loop limit and extends it to any measurement scheduling. For a costly, binary (on/off) sensor, we evaluate the optimal measurement protocol and derive physical bounds on the maximum net gain that can be extracted from thermal fluctuations. We show the emergence of deadline-induced blindness, a phenomenon where all measurements cease as the deadline approaches regardless of their cost. Taking the infinite-horizon limit, we find the exact periodic measurement schedules for the steady state as a function of the measurement cost $C$ and derive the macroscopic velocity envelopes beyond which viscous drag forces the engine into a net-dissipative regime. Finally, we generalize the results to a variable-precision sensor.