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?