1. Misplaced Idealizations Maxwell's Demon does not Compute John D. Norton Department of History and Philosophy of Science Center for Philosophy of Science University of Pittsburgh 1 4th Tuebingen Summer School in History and Philosophy of Science, July 2015

2. This Lecture 2 The quickest, simplest, clearest, most effective exorcism of Maxwell’s demon in 150 years. No information talk. No entropy cost of gaining information. No entropy cost of erasing information. No entropy cost of processing information. No Szilard’s Principle. No Landauer’s Principle. etc. Maxwell’s demon is not idealized well as an information processor or computing device.

3. The Exorcism in Brief (for experts) 3 Describe what a naturalized must demon do. demon any equilibrium system most of phase space 1. Attribute obvious properties to demon and system. Hamiltonian dynamics… 2. Find that the demon must violate Liouville theorem (conservation of phase volume). 3. same demon state out-of-equilibrium system a tiny part of phase space A quantum version. 4.

4. Maxwell demons of the fluctuation era 1905-1929 were not computers 4

5. Maxwell’s demon lives in the details of Brownian motion and other fluctuations Could these momentary, miniature violations of the second law be accumulated to large-scale violations? A real Maxwell’s demon? Guoy (1888), Svedberg (1907) designed mini- machines with that purpose. 5 “[…] we see under our eyes now motion transformed into heat by friction, now heat changed inversely into motion, and that without loss since the movement lasts forever. This is the contrary of the principle of Carnot. If this be so, to see the world return backward, we no longer have need of the infinitely keen eye of Maxwell's demon; our microscope suffices.” Poincaré, 1904

6. Guoy’s Proposal, 1888 6 The first “Brownian ratchet.” To and fro Brownian motion of a small body… thread …is rectified by a ratchet that can only turn one way.

7. Casing heats Colloid cools Svedberg’s Proposal 1907 7 Svedberg, The. “Über die Bedeutung der Eigenbewegung der Teilchen in kolloidalen Lösungen für die Beurteilung der Gültigkeitsgrenzen des zweiten Haupsatzes der Thermodynamik”.Annalen der Physik, 59 (1907) pp. 451–458. Charged colloid particles radiate their thermal energy. Tuned lead casing absorbs the radiation. …plus many more layers, details designed to prevent return of heat.

8. Marian Smoluchowski, 1912 8 Exorcism of Maxwell’s demon by fluctuations. Trapdoor hinged so that fast molecules moving from left to right swing it open and pass, but not vice versa. The second law holds on average only over time. Machines that try to accumulate fluctuations are disrupted fatally by them. BUT The trapdoor must be very light so a molecule can swing it open. AND The trapdoor has its own thermal energy of kT/2 per degree of freedom. SO The trapdoor will flap about wildly and let molecules pass in both directions.

9. Marian Smoluchowski, 1912 9 Other examples of defeated demons. The second law holds on average only over time. Machines that try to accumulate fluctuations are disrupted fatally by them. Guoy’s Brownian particle replaced by Brownian motion of the toothed wheel. Later popularized by Feynman Ambient voltage fluctuations electric current resistor heated above surrounding temperature

10. Is a Maxwell Demon Possible? 10

11. Nanotechnology now manipulates individual atoms 11 Molecules of CO on surface manipulated individually by scanning tunneling microscopes at -260C. https://www.youtube.com/watch?v=oSCX78-8-q0

12. Micron Scale Magnetic Brownian Ratchet 12 http://physics.aps.org/story/v26/st22

13. Micron Scale Magnetic Brownian Ratchet 13 http://physics.aps.org/story/v26/st22 “ A micron-scale bead in water is driven across a magnetic surface by an external magnetic field (pointing out of the screen and to the right) oscillating at about 20 Hz. Diffusion in the vertical direction is about 4000 times that expected of an undriven particle.”

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17. 17 “Any physically meaningful model of a Brownian motor must be compatible with the limitations that the second law imposes on its efficiency. In fact, a major part of the present paper is devoted to prove this compatibility for wide classes of models, and to explore how the entropy production S prod can be reduced in order to devise efficient motors.” p. 181 “Any physically meaningful model of a Brownian motor must be compatible with the limitations that the second law imposes on its efficiency. In fact, a major part of the present paper is devoted to prove this compatibility for wide classes of models, and to explore how the entropy production S prod can be reduced in order to devise efficient motors.” p. 181

18. Micron-machines designed by evolution 18 Electron micrograph of ribosome Schematic of protein synthesis Powered by ATP Evolution has not produced micro Maxwell’s demons in spite of the obvious evolutionary advantage.

19. The New Exorcism 19 Based on Section 4 of John D. Norton, "All Shook Up: Fluctuations, Maxwell's Demon and the Thermodynamics of Computation" Entropy, 15 (2013), pp. 4432-4483.

20. Assumptions used in the Exorcism 20

21. What a Maxwell Demon Does 21 demon any equilibrium system same demon state out-of-equilibrium system “intermediate state” Assumption (a) A Maxwell’s demon is a device that, when coupled with a thermal system in its final equilibrium state, will, over time, assuredly or very likely lead the system to evolve to one of the intermediate states; and, when its operation is complete, the thermal system remains in the intermediate state. Succeeds with all but small fraction  of equilibrium systems.

22. Demon cycles, Isolation 22 Assumption (b) The device returns to its initial state at the completion of the process; and it operates successfully for every microstate in that initial state. demon “device” demon “device” Assumption (c) The device and thermal system do not interact with any other systems.

23. Constitution of the Demon and the Thermal System 23 Assumption (d) The time evolution of the total system is Hamiltonian with a time-reversible, time- independent Hamiltonian. for canonical generalized momenta p 1, p 2, p 3, … and positions q 1, q 2, q 3, … Loosely speaking: The thermal system and demon have “generic” microdynamics. Not inviolable… but relaxing it quickly violates the Second Law. Zhang and Zhang “pressure demon.”

24. Hamiltonian Flow in Phase Space 24 Each point in phase space is a complete system. Trajectory is the complete history of the evolution of the system from start to finish.

25. Thermal Equilibrium States 25 …occupy virtually all of phase space. Hence most trajectories starting in non- equilibrium states end up in equilibrium states.

26. Thermal Equilibrium States 26 V Assumption (e) The equilibrium states occupy all but a tiny portion α of the thermal system’s phase space, V, where α is very close to zero. Assumption (f) The intermediate states are all within the small remaining volume of phase space, αV.

27. Liouville Theorem 27

28. Conservation of Phase Volume under Hamiltonian Flow 28

29. The Contradiction that completes the reductio 29

30. Impossible Compression 30

31. fraction over which demon succeeds thermal system phase volume thermal system must end up in non- equilibrium volume. demon phase volume (stays constant) demon phase volume (stays constant) Contradiction 31 Hamiltonian evolution of system + demon large phase volume v(1-  )(1-  )V much smaller phase volume v  V Liouville theorem Phase volume is conserved under Hamiltonian time development.

32. Robustness 32

33. What the Exorcism Does Not Do… 33 The second law of thermodynamics is not assumed. All is microphysics AND the assumption that equilibrium states fills the phase space. The circularity troubling the information theoretic exorcisms does not arise. (Sound vs profound dilemma.)

34. Recovering the approach to equilibrium is hard since we must show a small volume of non-equilibrium states evolves to a large volume of equilibrium states. Coarse graining saves the day. (1-  )(1-  )V contains all microstates upon which the demon can successfully act. Showing compression fails is the easy problem. What the Exorcism Does Not Do… 34 The volumes of phase space representing states are not coarse grained.

35. What the Exorcism Does Not Do… 35 Thermodynamic entropy is not included in the argumentation. It could be added if we are careful. But many are not and entropy talk more often confuses than not.

36. Quantum Exorcism 36

37. Nanoscale objects are quantum mechanical 37

38. Classical 38 Quantum States form a phase space of dimension 2n Momentum coordinates p 1, …, p n Configuration coordinates q 1, …, q n Time evolution is governed by Hamilton’s equations: n is very large: ~10 24 for ordinary macroscopic systems The system state |  (t)> is a vector in an n dimensional Hilbert space, with orthonormal basis vectors |e 1 >, …, |e n >. Time evolution is governed by Schroedinger’s equation:

39. Low Entropy State 39 n molecule gas confined to half of chamber State is in small 1/2 n th volume of phase space classical Classical Liouville theorem: phase volume is conserved. Quantum Liouville theorem: subspace dimension is conserved. State is in small dimensional subspace of Hilbert space quantum

40. Concluding Morals 40

41. How was such an easy exorcism overlooked? 41 Information enthusiasts were too fixated on making the information-based analysis work. Information skeptics were too fixated on showing that the information-based analysis fails. ? ? ? ? ? ? ? Our idealizations have been tracking fads.

42. 1950s: Information! 42 Claude Shannon (1948). "A Mathematical Theory of Communication” Bell Systems Technical Journal 27(1948), pp. 379-423, 623-656. Information ideas and concepts Entropy heat, work, thermodynamics = Worth trying, but how long do try before you give up?

43. Szilard’s Principle 43 Acquisition of one bit of information by the demon creates k ln 2 of thermodynamic entropy. Szilard 1929 Von Neumann 1932 Brillouin 1951+… Landauer’s Principle versus Landauer 1961 Bennett 1987+… Szilard’s principle is false. FALSE Erasure of one bit of information from a computer memory by the demon creates k ln 2 of thermodynamic entropy. Information vs Computation

44. 1970s: Computers! 44 “This essay is concerned with a particular philosophical view that holds that the mind literally is a digital computer (in a specific sense of “computer” to be developed), and that thought literally is a kind of computation.”

45. 1970s: Computers! 45 “I will show that the universe can be regarded as a giant quantum computer.”

46. 1970s: Computers! 46 http://www.technologyreview.com/view/429561/the-measurement- that-would-reveal-the-universe-as-a-computer-simulation/

47. 1970s: Computers! 47 =

48. Physics has principles… 48 … and so does computer science.

49. The End 49