Ever since J.C. Maxwell put forward the idea of an abstract being (‘a demon’) apparently being able to violate the second law of thermodynamics, it has served as a great source of inspiration and helped to establish important connections between statistical physics and information theory. The original version of the demon operates a trapdoor between two heat baths, such that a seemingly counterintuitive heat flow is established. Today, more generally, devices that are able to extract work from a single heat bath by rectifying thermal fluctuations are also called ‘Maxwell's demons’.
In this talk, we take a control-theoretic perspective and analyze a simple electrical model of the demon. In particular, we see how optimal control theory can be used to design a demon-like controller that optimally extracts work from thermal fluctuations. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be implemented using a variable capacitor and transformer. Hence, in contrast to many other studies, our demon is physically very concrete and operates continuously in time.
Henrik Sandberg received the M.Sc. degree in engineering physics and the Ph.D. degree in automatic control from Lund University, Lund, Sweden, in 1999 and 2004, respectively. He is an Associate Professor with the Automatic Control Laboratory, KTH Royal Institute of Technology, Stockholm, Sweden. From 2005 to 2007, he was a Post-Doctoral Scholar with the California Institute of Technology, Pasadena, USA. He has held visiting appointments with the Australian National University and the University of Melbourne, Australia. In 2013, he is a visiting scholar at the Laboratory for Information and Decision Systems (LIDS) at MIT, Cambridge, USA. His current research interests include secure networked control, power systems, model reduction, and fundamental limitations in control. Dr. Sandberg was a recipient of the Best Student Paper Award from the IEEE Conference on Decision and Control in 2004 and an Ingvar Carlsson Award from the Swedish Foundation for Strategic Research in 2007. He is currently an Associate Editor of the IFAC Journal Automatica.