Abstract
This morning session is devoted to problems of statistical physics, and I hope that together with my colleagues Dr Kac and Dr Cohen we will be able to show you that in this field very little is really understood, and that there remain quite general and fundamental problems which are still quite open. Since in fact even the formulation of these problems is often still controversial, let me begin with what I consider to be the basic task of statistical mechanics. It is, in my opinion, the elucidation of the relation between the microscopic, molecular description and the macroscopic description of the physical phenomena. This is illustrated in Fig. 1, where the microscopic description is divided according to wherther the classical or the more basic quantum theory is considered, and where only some of the macroscopic disciplines are shown. Note that I said relation and not explanation. I consider the two descriptions of nature as autonomous.
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References and Notes
The Poincaré theorem expresses the reversibility of the mechanical equations of motion. For a proof see for instance Chapter 1 of Lectures in Statistical Mechanics by G. E. Uhlenbeck and G. W. Ford, published by the American Mathematical Society, Providence, Rhode Island (1963). There one finds also a detailed discussion of this basic dilemma, which I have called the problem of Boltzmann.
An attempt of such an outline with a list of the unsolved problems I presented at the conference on Fundamental Problems in Statistical Mechanics, Vol. II, published by North-Holland Publishing Company, Amsterdam (1968), p. 1.
J. von Neumann, Z. Phys. 57, 30 (1929) [= Collected Works, Pergamon Press, New York (1961), Vol. I, p. 558].
W. Pauli and M. Fierz, Z. Phys. 106, 572 (1937) [= Collected Papers, Interscience Publishers, New York (1964), Vol. II, p. 797].
At this conference Onsager proposed that the vorticity in superfluid helium should be quantized in units h/m, which was shown to be true experimentally by Rayfield and Reif in 1963! The proceedings of the conference were published as a supplement to Vol. VI, Series IX of Nuovo Cimento in 1949. The discussions are still of great interest. Pauli’s remarks are on p. 166 (= Collected Papers, Vol. II, p. 1116.)
This would imply that the cause of the entropy increase would be quite different in quantum mechanics from the Gibbs phase mixing process in classical statistics.
I follow the discussion given in my Lectures in Statistical Mechanics, see note 1.
R. C. Tolman, The Principles of Statistical Mechanics, Oxford, The Clarendon Press (1938). Compare especially Chapter VI, Section 51 and Chapter XII A.
Compare P. Ehrenfest, Collected Papers, North-Holland Pubi. Comp. Amsterdam (1959), p. 353.
Note that because one has a coarse-grained distribution, the sum over the N% is really an integral.
See for instance E. Schròdinger, Statistical Thermodynamics, Cambridge University Press, Cambridge (1967), p. 67.
Also called the fountain effect. See J. F. Allen and A. D. Misener, Proc. Roy. Soc. London A 172, 467 (1939) and especially P. Kapitza, J. Phys. U.S.S.R. 5, 59 (1941), Phys. Rev. 60, 354 (1941).
J. D. Reppy and D. Depatie, Phys. Rev. Letters 12, 187 (1964). For another version of the experiment see H. Kojima, W. Veith, S. Putterman, E. Guyon and I. Rudnick, Phys. Rev. Letters 27, 714 (1971).
L. D. Landau, J. Phys. U.S.S.R. 5, 71 (1941) [= Collected Papers, Gordon and Breach, New York (1965), p. 301].
I. M. Khalatnikov, An Introduction to the Theory of Superfluidity, W. A. Benjamin, New York (1965), Ch. 9. In this book the paper of Landau quoted in 14 is also reprinted.
G. W. Rayfield and F. Reif, Phys. Rev. Letters 11, 305 (1963); Phys. Rev. 136, A 1194 (1964).
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© 1973 D. Reidel Publishing Company, Dordrecht-Holland
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Uhlenbeck, G.E. (1973). Problems of Statistical Physics. In: Mehra, J. (eds) The Physicist’s Conception of Nature. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2602-4_25
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