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Information thermodynamics for a feedback control with time delay

NSPCS14, KIAS, July 8-11, 2014. Information thermodynamics for a feedback control with time delay. Chulan Kwon Myongji University, Korea ckwon@mju.ac.kr. In collaboration with Jaegon Um, Uni-Wuerzburg , Germany Jae Dong Noh, University of Seoul, Korea Hyunggyu Park, KIAS, Korea.

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Information thermodynamics for a feedback control with time delay

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  1. NSPCS14, KIAS, July 8-11, 2014 Information thermodynamics for a feedback control with time delay Chulan Kwon Myongji University, Korea ckwon@mju.ac.kr In collaboration with Jaegon Um, Uni-Wuerzburg, Germany Jae Dong Noh, University of Seoul, Korea Hyunggyu Park, KIAS, Korea Feedback control: the exorcism of Maxwell’s demon Post-measurement process Multi-step feedback control with time delay Cold damping Summary

  2. I. Feedback control: the exorcism of a Maxwell’s demon The paradox of Maxwell’s demon: the violation of 2nd law -- Maxwell (1867), Szilard (1929), Landauer(1961), …. Szilard engine Incomplete exorcism • Demonic entropy • The state of demon? • Landauer’s principle • Nothing to do with the system’s time evolution

  3. used empty 2. Feedback control erased Hidden process Bit information process erasure measurement system state measurement outcome memory state feedback protocol, external field Post-measurement process observable Fluctuation theorem Generalized 2nd law T. Sagawa and M. Ueda, PRL (2012); NJP (2013) Proper exorcism of Maxwell’s demon

  4. II. Fluctuation theorem for post-measurement process Schematic view Measurement 1 0 measurement feedback Post-measurement

  5. Probability of measurement outcome given system state Post-measurement process by feedback control

  6. Schnackenberg, 1976, master equation Environmental entropy production trajectory time-reverse trajectory anomalous entropy production due to odd-parity force

  7. Total entropy production Fluctuation Theorem Mutual information

  8. more correlation, more information Less correlation, less information lower entropy higher mutual information at measurement higher entropy lower mutual information in post-measurement

  9. III. Multi-step feedback control with time delay

  10. Total entropy production Fluctuation theorem Generalized 2nd law

  11. IV. Cold damping Kim & Qian, PRL, 2007; Jourdan et al, Nanotechnology, 2007; Ito & Sano, PRE, 2011 y E feedback v v measure

  12. V. Summary • The paradox of Maxwell’s demon is resolved by the information • thermodynamics of the feedback control. • The observable post-measurement process satisfies the fluctuation theorem, • which is the true exorcism of Maxwell’s demon, with no knowledge about • hidden process in Maxwell’s demon or memory device such as • measurement, erasure. • The multi-step feedback control with time delay is studied: • The cold damping problem is revisited. Temperature depends on time delay • and time interval between measurement steps. • An experimental study is expected.

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