Energetic cost of feedback control
Jannik Ehrich, Susanne Still, David A. Sivak
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.