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Physics of Information
Yovav Kalifon
Weizmann 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.
Physics of Information
•Making a measurement
Physics of Information
•What is information?
Physics of Information
•Information processing
• Exorcise Maxwell’s (mechanical) demon
• Consider intelligent beings as demons
• “Universal law” of measurements
Second Law of Thermodynamics
Second Law of Thermodynamics
Maxwell:
“The 2nd law is only statistically valid.
“Could statistical fluctuations be
exploited to run a perpetual motion
machine?”
Maxwell’s Demon
Exploiting fluctuations
Ratchet and pawl
Getting hit means Getting heat!
Forward Step
Stretch
ε
Lift
Lθ
Fluctuation
Lθ+ε
Forward Step Rate
Stretch
ε
Lift
Lθ
Fluctuation
Lθ+ε
Backward Step
Fluctuation
ε
Drop
Lθ
Release
Lθ+ε
Backward Step Rate
Fluctuation
ε
Drop
Lθ
Release
Lθ+ε
Reversible process
The engine keeps 2nd law
Trap door demon
Mechanical demons fluctuate
Ranque-Hilsch vortex tube (1933)
Szilard:
“Under what circumstances could
we construct a perpetual motion
machine, utilizing intelligent
beings?”
Concerns of intelligent demons
Concerns of intelligent demons
Making measurements
Processing information
Erasing information
Szilard’s first machine
Intelligent being couples parameters
Szilard’s first machine
Work done at the expense of heat
ENTROPY BILL
• Ideal gas:
• Heat reservoir:
ENTROPY BILL
• The frequency of each outcome:
• Overall we get:
ENTROPY BILL
• Ansatz:
• Overall we get:
Szilard’s second machine
Szilard’s second machine
ENTROPY BILL
• If parameter (x) thermalizes reversibly:
• Ansatz:
ENTROPY BILL
• Overall we get:
• Szilard’s Universal Law:
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
Szilard’s third machine
Szilard’s third machine
Szilard’s third machine
Szilard’s third machine
Szilard’s third machine
ENTROPY BILL
ENTROPY BILL
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
Summary
• Szilard assumes the 2nd law
• A “universal law” of measurements
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.
So what is intelligence?
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