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IDSS Special Seminars

A Hamiltonian Demon: Circumventing the Second Law by Quantizing Energy

February 17, 2023 @ 2:30 pm - 3:30 pm

Raffaello D'Andrea (ETH Zürich)



In this talk I will introduce a deterministic process, henceforth referred to as a demon, for altering the equilibrium distribution of a billiards-like dynamical system. The system consists of particles whose energies are integer valued, and where all energy-exchange mechanisms preserve this quantization.  As a result, time and positions are continuous, while velocities are discrete. The demon is a localized, velocity-dependent potential whose effect is to simply alter the direction of an incident particle.  It is shown how the demon can steer the system away from equilibrium to create a temperature differential, a density differential, a circulation, and a large-scale oscillation.  It is further shown how the system — including the demon — can be captured by a time-independent Hamiltonian, where the set of states whose energies are integer valued is an invariant set. In addition, given any finite time horizon, the novel behavior extends to continuous energies in a neighborhood of the invariant set. Since the set of states where energy is quantized has zero Lebesgue measure, the results are not inconsistent with statistical characterizations of the second law of thermodynamics.

The talk is based on classical results which are over 100 years old and extensive computer simulations. It should be accessible to any (motivated) student with a bachelor’s degree in engineering, physics, mathematics, or computer science.


Raffaello D’Andrea is a professor at ETH Zürich and the founder/CEO of Verity. He cofounded Kiva Systems, which was acquired by Amazon and rebranded as Amazon Robotics. During his time as a professor at Cornell University, he cofounded the systems engineering program and led the Cornell Robot Soccer team to four world championships. He is also a founder of RoboGlobal, home to the world’s first Robotics and AI Exchange Traded Fund.

His work as a new media artist has been exhibited at the Venice Biennale and is part of the permanent collections of the National Gallery of Canada and France’s FRAC Centre.  He created the drone design and choreographies for Cirque du Soleil’s Paramour on Broadway and Metallica’s WorldWired tour, and was executive producer for the drone light shows in Drake’s Aubrey & the Three Migos tour, Céline Dion’s Courage tour, and Justin Bieber’s Justice tour.  He is the co-creator of the Robotic Chair, a plain-looking wooden chair that falls apart and seems to defy the second law of thermodynamics by reassembling itself.  Other creations include Cubli, the Balancing Cube, the Distributed Flight Array, the Blind Juggler, and the Flying Machine Arena.

In 2020 he was inducted into the National Inventors Hall of Fame and was elected to the U.S. National Academy of Engineering.  His TED and research videos, with tens of millions of views, offer an inspiring view into the world of engineering, robotics, and computer science.

MIT Institute for Data, Systems, and Society
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139-4307