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.

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.

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 DemonExploiting fluctuations

Ratchet and pawl

Getting hit means Getting heat!

Forward Step

Stretchε

LiftLθ

FluctuationLθ+ε

Forward Step Rate

Stretchε

LiftLθ

FluctuationLθ+ε

Backward Step

Fluctuationε

DropLθ

ReleaseLθ+ε

Backward Step Rate

Fluctuationε

DropLθ

ReleaseLθ+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?