Maxwell’s Demon John D. Norton Department of History and Philosophy of Science Center for Philosophy of Science Universi

1. Maxwell’s DemonJohn D. NortonDepartment of History and Philosophy of ScienceCenter for Philosophy of ScienceUniversity of Pittsburgh

2. 483, 187–189 (08 March 2012)

3. Consensus reported The paradox of the apparent violation of the second law [by a Maxwell’s demon] can be resolved by noting that during a full thermodynamic cycle, the memory of the demon, which is used to record the coordinates of each molecule, has to be reset to its initial state. Indeed, according to Landauer’s principle, any logically irreversible transformation of classical information is necessarily accompanied by the dissipation of at least kT ln(2) of heat per lost bit (about 3x10-21 J at room temperature (300 K)), where k is the Boltzmann constant and T is the temperature. …This entropy cost required to reset the demon’s memory to a blank state is always larger than the initial entropy reduction, thus safeguarding the second law. Landauer’s principle hence seems to be a central result that not only exorcizes Maxwell’s demon, but also represents the fundamental physical limit of irreversible computation.

4. 1867

5. The original conception Divided chamber with a kinetic gas. Demon operates door intelligently J. C. Maxwell in a letter to P. G. Tait, 11th December 1867 “…the hot system has got hotter and the cold system colder and yet no work has been done, only the intelligence of a very observant and neat-fingered being has been employed.” “[T]he 2nd law of thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea you cannot get the same tumblerful of water out again.”

6. 1905

7. Einstein’s Brownian Motion Paper "On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat.” Annalen der Physik, 17(1905), pp. 549-560. (May 1905; received 11 May 1905) Thermal fluctuations in small particles suspended in liquids should be microscopically visible and enable an estimation of Loschmidt’s number. Thermal process must be analysed by the molecular-kinetic theory of heat. There really are atoms.

8. “…no longer strictly valid…” “If it is really possible to observe the motion discussed here …” “… then classical thermodynamics can no longer be viewed as strictly valid even for microscopically distinguishable spaces....” “… … and an exact determination of the real size of atoms becomes possible.”

9. 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.

10. 1907

11. Svedberg, The (1907). “Über die Bedeutung der Eigenbewegung der Teilchen in kolloidalen Lösungen für die Beurteilung der Gültigkeitsgrenzen des zweiten Haupsatzes der Thermodynamik,” Annalen der Physik, 59, pp.451-58.

12. 1912

13. 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.

14. Smoluchowski’s original version. The one-way valve demon

15. Other examples of defeated demons. Later popularized by Feynman

16. Other examples of defeated demons.

17. Marian Smoluchowski, 1912 The second law holds on average only over time. Machines that try to accumulate fluctuations are disrupted fatally by them. quote:

18. Marian Smoluchowski, 1912 “Indeed you would be just as mistaken if you wanted to warm a certain part of a fluid by friction through the Brownian molecular motion of suspended particles by means of threads.” “… it appears at present that the construction of a perpetual motion machine that produces work continuously is excluded not by purely technical difficulties, but as a matter of principle.” “Naturally this brief exposition should only serve to make this assertion physically plausible. For a proper proof one can consult the presentations of statistical mechanics. In any case, the latter turn out still to have some deficiencies…”

19. What about an intelligently operating demon? Smoluchowski’s proposal

20. It won’t work, since the operating demon is a physical system…

21. Smoluchowski opens the door…

22. 1929Szilard’sOne-Molecule Engine

23. Simplest case of fluctuations Many molecules A few molecules One molecule Can a demon exploit these fluctuations?

24. The One-Molecule Engine Szilard 1929 A partition is inserted to trap the molecule on one side. Initial state Work kT ln 2 gained in raising the weight. It comes from the heat kT ln 2, drawn from the heat bath. The gas undergoes a reversible, isothermal expansion to its original state. Net effect of the completed cycle: Heat kT ln 2 is drawn from the heat bath and fully converted to work. The total entropy of the universe decreases by k ln 2. The Second Law of Thermodynamics is violated.

25. The One-Molecule Engine Szilard 1929 A partition is inserted to trap the molecule on one side. Initial state Work kT ln 2 gained in raising the weight. It comes from the heat kT ln 2, drawn from the heat bath. The gas undergoes a reversible, isothermal expansion to its original state. Net effect of the completed cycle: Heat kT ln 2 is drawn from the heat bath and fully converted to work. The total entropy of the universe decreases by k ln 2. The Second Law of Thermodynamics is violated.

26. Szilard’s escape

27. The Information-Theoretic Turn

28. Szilard’s Principle Landauer’s Principle versus Szilard 1929 Von Neumann 1932 Brillouin 1951+… Landauer 1961 Bennett 1987+… Acquisition of one bit of information by the demon creates k ln 2 of thermodynamic entropy. Szilard’s principle is false. Erasure of one bit of information by the demon creates k ln 2 of thermodynamic entropy. Real entropy cost only taken when the naturalized demon erases the memory of the position of the molecule. FALSE

29. The Standard Erasure Procedure Model of binary memory. One molecule gas in a divided chamber. Heat kT ln 2 Entropy k ln 2 passes to environment.