Towards a thermodynamics of control: Entropy, energy and Kalman filtering

We propose a method to analyse the flows of information and energy between two systems (plant and controller) connected in feedback. Extending a work by Touchette and Lloyd (2000, 2004), we estimate the advantage, both in terms of entropy reduction and energy extraction, of a feedback controller over an open-loop control in terms of the information on the plant state that is available to the controller. By energy here we mean any objective function that we seek to minimize, for example the square of the state. We apply this methodology on the Kalman filter, and develop a physical interpretation comparable to Mitter and Newton´s (2005).