Energetic cost of feedback control

TL;DR

This paper explores the energetic costs of feedback control in small systems, highlighting how physical interactions and nonreciprocal effects influence the work needed to maintain control, with implications for thermodynamics and system design.

Contribution

It introduces a minimally dissipative controller model and analyzes how nonreciprocal interactions affect the energetic cost of feedback control.

Findings

Work required compensates for entropy decrease during control

Nonreciprocal interactions simplify the analysis of control costs

Controller design impacts the thermodynamic efficiency of feedback systems

Abstract

Successful feedback control of small systems allows for the rectification of thermal fluctuations, converting them into useful energy; however, control itself requires work. This paper emphasizes the fact that the controller is a physical entity interacting with the feedback-controlled system. For a specifically designed class of controllers, reciprocal interactions become nonreciprocal due to large timescale separation, which considerably simplifies the situation. We introduce a minimally dissipative controller model, illustrating the findings using a simple example. We find that the work required to run the controller must at least compensate for the decrease in entropy due to the control operation.