  Feedback control mechanisms are ubiquitous in science and technology, and
play an essential role in regulating physical, biological and engineering
systems. The standard second law of thermodynamics does not hold in the
presence of measurement and feedback. Most studies so far have extended the
second law for discrete, Markovian feedback protocols; however, non-Markovian
feedback is omnipresent in processes where the control signal is applied with a
non-negligible delay. Here, we experimentally investigate the thermodynamics of
continuous, time-delayed feedback control using the motion of an optically
levitated, underdamped microparticle. We test the validity of a generalized
second law which bounds the energy extracted from the system and study the
breakdown of feedback cooling for very large time delays.
