i.feedback control: the exorcism of maxwell’s demon ii.post-measurement process iii.multi-step...
TRANSCRIPT
Information thermodynamics for a feedback control
with time delay
I. Feedback control: the exorcism of Maxwell’s demonII. Post-measurement processIII. Multi-step feedback control with time delayIV. Cold dampingV. Summary
NSPCS14, KIAS, July 8-11, 2014
In collaboration withJaegon Um, Uni-Wuerzburg, Germany
Jae Dong Noh, University of Seoul, KoreaHyunggyu Park, KIAS, Korea
Chulan KwonMyongji University, Korea
I. Feedback control: the exorcism of a Maxwell’s demon
1. The paradox of Maxwell’s demon: the violation of 2nd law -- Maxwell (1867), Szilard (1929), Landauer(1961), ….
Szilard engine
• Demonic entropy The state of demon? • Landauer’s principle Nothing to do with the system’s time evolution
Incomplete exorcism
2. Feedback control
feedback
measurement
measurement outcome
system state
protocol, external field
erasure
empty usederased
Hiddenprocess
memory state
Post-measurement process observable
Fluctuation theorem
PROPER EXORCISM OF MAXWELL’S DEMON
Bitinformation process
Generalized 2nd law T. Sagawa and M. Ueda, PRL (2012); NJP (2013)
II. Fluctuation theorem for post-measurement process
measurement feedback
10
Measurement
Post-measurement
Schematic view
Probability of measurementoutcome given system state
Post-measurement processby feedback control
Environmentalentropy production
trajectory
time-reverse trajectory
anomalous entropy production due to odd-parity force
Schnackenberg, 1976, master equation
Total entropy production
Fluctuation Theorem
Mutualinformation
Less correlation, less information
higher entropylower mutual information in post-measurement
more correlation, more information
lower entropyhigher mutual information at measurement
III. Multi-step feedback control with time delay
Total entropy production
Fluctuation theorem
Generalized 2nd law
IV. Cold damping
E
v
y
measure
Kim & Qian, PRL, 2007; Jourdan et al, Nanotechnology, 2007; Ito & Sano, PRE, 2011
feedback
v
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.