Entropy reduction via communications in cyber physical systems: How to feed maxwell´s demon?

In order to understand how to operate the physical dynamics of cyber physical systems (CPSs), we study the control of entropy (or equivalently uncertainty) via communications in CPSs. We consider the controller as the Maxwell´s demon that decimates the system entropy. Due to the second law of thermodynamics, the system entropy cannot be spontaneously decreased. Therefore, to reduce the system entropy, the controller needs external information communicated from sensors. For a finite state physical system in CPS, we derive upper and lower bounds for the communication requirements. The optimal designs of message mechanism and control policy are proposed.