Müller I. A history of thermodynamics. The doctrine of energy and entropy (1185104), страница 26
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Gibbs: “On the equilibrium of heterogeneous substances.” Transactions of theConnecticut Academy 3 (1876) p. 229.49 To those who know the chain of command in German universities – particularly in the19th century – it is inconceivable that Zermelo entered into a major discussion with acelebrity like Boltzmann without the approval and encouragement of his mentor Planck.Actually Planck was notoriously slow to accept new ideas, including his own, cf.
Chap. 7.50 Later Zermelo even helped to make statistical mechanics known among physicists byediting a German translation of Gibbs’s “Elementary principles of statistical mechanics”,see below.51 H. Poincaré: „Sur le problème des trois corps et les équations de dynamique’’ [On thethree-body problem and the dynamical equations] Acta mathematica 13 (1890) pp.1–270.See also : H. Poincaré: “Le mécanisme et l’expérience’’ [Mechanics and experience]Revue Métaphysique Morale 1 (1893) pp. 534–537.106 4 Entropie as S = k ln Winitial position.
Clearly therefore, the entropy which, after all, is a functionof the atomic positions, cannot grow monotonically. This became known asthe recurrence objection. Actually, Zermelo thought that the fault lay inmechanics, because he considered irreversibility to be too well establishedto be doubted. But he could not bring himself to accept any of Boltzmann’sprobabilistic arguments.52In the controversy Boltzmann tried at first to get away with theobservation that it would take a long time for a recurrence to occur.Zermelo agreed, but declared the fact irrelevant.
The publicly conducteddiscussion53,,54,,55,,56 then focussed on Boltzmann’s assertion that – at any onetime – there were more initial conditions leading to entropy growth than toentropy decrease. Zermelo could not understand that assumption, and heridiculed it. In fact, however, something possibly profound came out of thediscussion.
Boltzmann conceded the point – without ever admitting it in somany words (!) – when he speculated that… in the universe, which is nearly everywhere in an equilibrium, andtherefore dead, there must be relatively small regions of the dimensions ofour star space (call them worlds) … which, during the relatively shortperiods of eons, deviate from equilibrium and among these [there must be]equally many in which the probability of states increases and decreases.
…A creature that lives in such a period of time and in such a world willdenote the direction of time toward less probable states differently than thereverse direction: The former as the past, the beginning, the latter as thefuture, the end. With that convention the small regions, worlds, will“initially” always find themselves in an improbable state.Thus, over all worlds the number of initial conditions for growth anddecay of entropy may indeed be equal, although in some single world theyare not. It seems that Boltzmann believed that the universe as a whole isessentially in equilibrium, but with occasional fluctuations of the size and5253545556Ten years later Zermelo must have reconsidered this position.
In 1906 he translatedGibbs’s memoir on statistical mechanics into German, and surely he would not haveundertaken the task if he had still thought statistical or probabilistic arguments to beunimportant. Zermelo’s translation helped to make Gibbs’s statistical mechanics known inEurope.E. Zermelo: “Über einen Satz der Dynamik und die mechanische Wärmelehre” [On atheorem of dynamics and the mechanical theory of heat] Annalen der Physik 57 (1896)pp.
485–494.L. Boltzmann: “Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn. E.Zermelo” [Reply to the considerations of Mr. E. Zermelo on the theory of heat] Annalender Physik 57 (1896) pp. 773–784.E. Zermelo: “Über mechanische Erklärungen irreversibler Vorgänge. Eine Antwort aufHrn. Boltzmanns “Entgegnung”.
[“On mechanical explanations of irreversible processes.A response to Mr. Boltzmann’s “reply”] Annalen der Physik 59 (1896), pp. 392–398.L. Boltzmann: “Zu Hrn. Zermelos Abhandlung “Über die mechanische Erklärungirreversibler Vorgänge” [On Mr. Zermelo’s treatise “On the mechanical explanation ofirreversible processes”] Annalen der Physik 59 (1896) pp.
793–801.Maxwell Demon107duration of our own big-bang-world. A fluctuation will grow away fromequilibrium for a while and then relax back to equilibrium. In both cases thesubjective direction of time – as seen by a creature – is toward equilibrium,irrespective of the fact that the growing fluctuation objectively moves awayfrom equilibrium. In order to make that mind-boggling idea more plausible,Boltzmann57 draws an analogy to the notions of up and down on the earth:Men in Europe and its antipodes both think that they stand upright, whileobjectively one of them is upside down. Applied to time, however, the ideadoes not seem to have gained recognition in present-day physics; it isignored – at least outside science fiction.
Maybe rightly so (?).Boltzmann tries to anticipate criticism of his daring concept of time andtime reversal by saying:Surely nobody will consider a speculation of that sort as an importantdiscovery or – as the old philosophers did – as the highest aim of science.It is, however, the question whether it is justified to scorn it as somethingentirely futile.Actually we may suspect that Boltzmann was not entirely sincere whenhe made that disclaimer. Indeed, in the years to come he is on record forrepeating his cosmological model several times. After having invented it inthe discussion with Zermelo he repeats it, and expands on it in his book onthe kinetic theory, and again in his general lecture at the World Fair inSt.
Louis58.All in all, the discussion between Boltzmann and Zermelo – despiteconsiderable acrimony – was conducted on a high level of sophisticationwhich definitely sets it off from the more pedestrian attempts of Maxwelland Kelvin to come to grips with randomness and probability. Thoseattempts involved the Maxwell demon.Maxwell DemonMaxwell invented the demon59 in the effort to reconcile the irreversibility inthe trend toward a uniform temperature with the kinetic theory: … acreature with such refined capabilities that it can follow the path of eachatom.
It guards a slide valve in a small passage between two parts of a gaswith – initially – equal temperatures. The demon opens and closes the valveso that it allows fast atoms from one side to pass, and slow atoms to pass57L. Boltzmann: (1898) loc. cit. p.129.L. Boltzmann: “Über die statistische Mechanik” [On statistical mechanics] Lecture givenat a scientific meeting in connection with the World Fair in St.
Louis (1904). See also:E. Broda (1979) loc.cit. pp. 206–224.59 According to G. Peruzzi (2000) loc.cit. p. 93 f. the demon was first conceived in a letterby Tait to Maxwell in (1867). It appeared in print in Maxwell’s “Theory of Heat”Longmans, Green & Co. London (1871).58108 4 Entropie as S = k ln Wfrom the other side. In this manner it creates a temperature differencewithout work because, indeed, the valve has very little mass.The Maxwell demon was – and is – much discussed, primarily, I suspect,because it can happily be talked about by people who do not possess theslightest knowledge of mathematics. In the works of Kelvin60 the notionreached absurd proportions: He invented … an army of intelligent Maxwelldemons which is stationed at the interface between a cold and a hot gas and… equipped with clubs, molecular cricket bats, as it were.
… Its mass isseveral times as big as the molecules … and the demons must not leavetheir assigned places except when necessary to execute their orders.Enough of that! Brush61 recommends an article by Klein62 for the readerswho want to familiarize themselves with the voluminous secondaryliterature on Maxwell’s demon.
But we shall leave the subject as quickly aspossible. It has a touch of banality. We might just as well go into somebelly-aching over a demon that could improve our chances in a dice game.Boltzmann and PhilosophyThere is a persistent tale that Boltzmann committed suicide in a depressedmood, created by discouragement and lack of recognition of his work. Thiscannot be true.
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