physics of information yovav kalifon weizmann inst. 18 nov 2008 szilard, l. (1929) `on the decrease...
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Physics of Information
Yovav KalifonWeizmann Inst. 18 Nov 2008
Szilard, L. (1929) `On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings', Zeitschrift für Physik 53, 840¯856.
Feynman, Feynman Lectures on Physics, Ratchet and Pawl, Volume 1, Chapter 46.
Landauer, R. (1961) `Irreversibility and Heat Generation in the Computing Process', Advances in Chemical Physics 5, 183¯191.
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Physics of Information
•Making a measurement
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Physics of Information
•What is information?
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Physics of Information
•Information processing
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• Exorcise Maxwell’s (mechanical) demon
• Consider intelligent beings as demons
• “Universal law” of measurements
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Second Law of Thermodynamics
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Second Law of Thermodynamics
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Maxwell:
“The 2nd law is only statistically valid.
“Could statistical fluctuations be exploited to run a perpetual motion machine?”
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Maxwell’s DemonExploiting fluctuations
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Ratchet and pawl
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Getting hit means Getting heat!
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Forward Step
Stretchε
LiftLθ
FluctuationLθ+ε
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Forward Step Rate
Stretchε
LiftLθ
FluctuationLθ+ε
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Backward Step
Fluctuationε
DropLθ
ReleaseLθ+ε
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Backward Step Rate
Fluctuationε
DropLθ
ReleaseLθ+ε
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Reversible process
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The engine keeps 2nd law
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Trap door demon
Mechanical demons fluctuate
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Ranque-Hilsch vortex tube (1933)
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Szilard:
“Under what circumstances could we construct a perpetual motion machine, utilizing intelligent beings?”
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Concerns of intelligent demons
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Concerns of intelligent demons
Making measurements
Processing information
Erasing information
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Szilard’s first machine
Intelligent being couples parameters
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Szilard’s first machine
Work done at the expense of heat
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ENTROPY BILL
• Ideal gas:
• Heat reservoir:
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ENTROPY BILL
• The frequency of each outcome:
• Overall we get:
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ENTROPY BILL
• Ansatz:
• Overall we get:
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Szilard’s second machine
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Szilard’s second machine
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ENTROPY BILL
• If parameter (x) thermalizes reversibly:
• Ansatz:
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ENTROPY BILL
• Overall we get:
• Szilard’s Universal Law:
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The entropy of erasure
Landauer (1961) and Bennet (1982): • A measurement is essentially copying• Computation can be made reversible• Erasing memory means compressing the
phase space of possible physical states, inevitably heating up the environment
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Szilard’s third machine
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Szilard’s third machine
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Szilard’s third machine
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Szilard’s third machine
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Szilard’s third machine
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ENTROPY BILL
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ENTROPY BILL
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Summary• Simple demons fail due to Brownian motion
• Intelligent demons are a part of the system
• Demons make up for the missing entropy
• No perpetual motion machine is known
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Summary
• Szilard assumes the 2nd law
• A “universal law” of measurements
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Summary
• Szilard’s own work supports the claim that erasing memory is the only stage which necessarily raises the entropy of the system
• Inanimate automatic machines can measure parameters, store the information, process it, even print the result.
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So what is intelligence?