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Misplaced Idealizations: Maxwell's Demon does not Compute

This lecture challenges the commonly held belief that Maxwell's demon can function as an information processor or computing device. It provides a clear and effective argument that demonstrates the demon's limitations in terms of information and entropy. The lecture also explores alternative methods of exorcising Maxwell's demon using fluctuation phenomena and offers examples of defeated demons in various systems. The presentation concludes with a discussion on the compatibility of Brownian motors with the second law of thermodynamics and the absence of micro Maxwell's demons in evolutionary systems.

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Misplaced Idealizations: Maxwell's Demon does not Compute

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  1. Misplaced IdealizationsMaxwell's Demon does not ComputeJohn D. NortonDepartment of History and Philosophy of ScienceCenter for Philosophy of ScienceUniversity of Pittsburgh 4th Tuebingen Summer School in History and Philosophy of Science, July 2015

  2. This Lecture Maxwell’s demon is not idealized well as an information processor or computing device. 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. etc.

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

  4. Maxwell demonsof the fluctuation era1905-1929 werenot computers

  5. Maxwell’s demon livesin the details of Brownian motion and other fluctuations “[…] 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 Could these momentary, miniatureviolations 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.

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

  7. Svedberg’s Proposal 1907 Charged colloid particles radiate their thermal energy. Colloid cools Tuned lead casing absorbs the radiation. Casing heats …plus many more layers, details designed to prevent return of heat. 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.

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

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

  10. Is a Maxwell Demon Possible?

  11. Nanotechnology now manipulates individual atoms 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 http://physics.aps.org/story/v26/st22

  13. Micron Scale Magnetic Brownian Ratchet “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.” http://physics.aps.org/story/v26/st22

  14. “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 Sprod can be reduced in order to devise efficient motors.” p. 181

  15. Micron-machines designed by evolution 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.

  16. The New Exorcism 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.

  17. Assumptionsused in the Exorcism

  18. What a Maxwell Demon Does demon same demon state any equilibrium system 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 b of equilibrium systems.

  19. Demon cycles, Isolation Assumption (c) The device and thermal system do not interact with any other systems. demon “device” demon “device” 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.

  20. Constitution of the Demon and the Thermal System Assumption (d) The time evolution of the total system is Hamiltonian with a time-reversible, time-independent Hamiltonian. for canonical generalized momenta p1, p2, p3, … and positions q1, q2, q3, … 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.”

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

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

  23. Thermal Equilibrium States 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. V Assumption (f) The intermediate states are all within the small remaining volume of phase space, αV.

  24. Liouville Theorem

  25. Conservation of Phase Volume under Hamiltonian Flow

  26. The Contradictionthat completes the reductio

  27. Impossible Compression

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

  29. Robustness

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

  31. What the Exorcism Does Not Do… The volumes of phase space representing states are not coarse grained. (1-a)(1-b)V contains all microstates upon which the demon can successfully act. 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. Showing compression fails is the easy problem.

  32. What the Exorcism Does Not Do… 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.

  33. Quantum Exorcism

  34. Nanoscale objects arequantum mechanical

  35. Classical Quantum States form a phase space of dimension 2n Momentum coordinates p1, …, pn Configuration coordinates q1, …, qn The system state |y(t)> is a vector in an n dimensional Hilbert space, with orthonormal basis vectors |e1>, …, |en>. n is very large: ~1024 for ordinary macroscopic systems Time evolution is governed by Schroedinger’s equation: Time evolution is governed by Hamilton’s equations:

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

  37. Concluding Morals

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

  39. 1950s: Information! Claude Shannon (1948). "A Mathematical Theory of Communication” Bell Systems Technical Journal27(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?

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

  41. 1970s: Computers! “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.”

  42. 1970s: Computers! “I will show that the universe can be regarded as a giant quantum computer.”

  43. 1970s: Computers! http://www.technologyreview.com/view/429561/the-measurement-that-would-reveal-the-universe-as-a-computer-simulation/

  44. 1970s: Computers! =

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

  46. The End

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