References
- Physicists have only recently begun to realize that Sinai's theorem on the ergodicity of hard sphere systems, a significant landmark in modern ergodic theory, pertains to a subject that they once considered of the greatest importance
- Sinai , J. G. 1967 . Statistical Mechanics: Foundations and Applications , Edited by: Bak , T. 559 New York : Benjamin . See
- Wightman , A. S. 1971 . Statistical Mechanics at the Turn of the Decade , Edited by: Cohen , E. G. D. 1 New York : Marcel Dekker .
- 1967 . Arch. Hist. Exact Sci. , 4 : 145 For further details see my paper inon which most of this introduction is based
- Report of the 21st Meeting of the British Association at Ipswich . pp. 6. Although Waterston's paper on kinetic theory was not published until 1893, an abstract announcing the equipartition theorem was printed in the Transactions of the Sections
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- Brush , S. G. 1965 . Kinetic Theory , Vol. 1 , Oxford and New York : Pergamon Press . English translation reprinted in
- Maxwell , J. C. 1860 . Phil. Mag. [4] , 19 : 21 19, 20
- Brush , S. G. Kinetic Theory Vol. 1. , reprinted in part in
- 1965 . The Scientific Papers of James Clerk Maxwell , New York : Dover Publications . See
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- Jeans , J. H. 1901 . Phil. Mag. [6] , 4 : 585 It may be noted that the phrase “continuity of path,” which the Ehrenfests attributed to Maxwell, does not appear anywhere in this paper (or elsewhere in Maxwell's writings as far as I can determine). It was apparently first used by
- Boltzmann , L. 1871 . Sitzungsber, k. Akad. Wiss. Wien, K1. II , 63 : 679
- Boltzmann , L. 1884 . Sitzungsber. k. Akad. Wiss. Wien, K1. II , 90 : 231 This paper is discussed in a forthcoming historical study by Martin J. Klein
- 1968 . A single system that passes through all states on the energy surface was called isodisch , New York : Chelsea Pub. Co. . Boltzmann's term for ensemble was lnbegriff See the footnote on page 147, Volume III, in Boltzmann's Wissenschaftliche AbhandlungenBarth, Leipzig, 1909, reprinted by
- Boltzmann , L. 1887 . J. f. reine und angew. Math. , 100 : 201 This paper is sometimes cited as his first statement of the ergodic hypothesis, but as we have seen the word Ergode and the separate concept of an ergodic [isodic] system had been introduced earlier
- Boltzmann , L. 1892 . Sitzungsber. math.-phys. Cl. k. Bay. Akad. Wiss. München , 22 ( 3 ) : 329
- 1893 . Phil. Mag. [5] , 35 : 153
- 174 For further discussion on this point see of my paper cited in note 2
- Cantor , G. 1878 . J. f. reine und angew, Math , 84 : 242
- Cantor , Georg . 1915 . Contributions to the Founding of the Theory of thansfinite Numbers , Edited by: Jourdain , P. E. B. New York : Dover Publications . A convenient account of Cantor's work may be found in translated with introduction and notes by reprint of the edition)
- Peano , G. 1890 . Math. Ann , 36 : 157
- Hertz , P. 1910 . Ann. Phys. [4] , 33 : 225 537
- Brouwer , L. E. J. 1910 . Math. Ann. , 70 : 161
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- 1912 . Math. Ann. , 72 : 55
- Klein , M. J. 1962 . Arch. Hist. Exact Sci. , 1 : 459
- Kangro , Hans , ed. 1970 . Vorgeschichte des Planckschen Strahlungsgesetzes , Wiesbaden : Franz Steiner Verlag . a comprehensive account of the background of Planck's work has recently been published by
- Ehrenfest , P. 1911 . Ann. Phys , 36 : 91
- Klein , M. J. 1970 . Pad Ehrenfest , 245 – 251 . Amsterdam : North-Holland . see the discussion by
- Ehrenfest , P. and Ehrenfest , T. 1959 . The Conceptual Foundations of the Statistical Approach in Mechanices , Edited by: Moravcsik , M. J. 81 – 83 . Ithaca : Cornell University Press . Encykl. d. math. Wiss., Vol. IV, part 2, Article IV 32 (Teubner, Leipzig, 1911) For the circumstances of composition of this article, see Klein Ehrenfestand Chapter 6
- 31 – 32 . Ibid., in the original German article, or p. 22 of the English translation (which I have revised slightly, restoring italics in the original)
- Rosenthal , A. 1914 . Ann. Phys , 43 : 894
- For information about Plancherel and Rosenthal I am indebted to Jacqueline Walker (American Mathematical Society) and Frances Keegan (Purdue University)
- 1954 . Elements of Statistical Mechanics , 123 – 126 . New York : Rinehart . An exception is D. ter Haar 333, 355–360;
- 1966 . Elements of Thermostatistics , New York : Holt, Rinehart and Winston . although he gives substantial space to a discussion of the ergodic hypothesis, ter Haar still prefers the ensemble approach, and in the second edition most of this material has been removed: see
- Tolman , R. C. 1938 . The Principles of Statistical Mechanics , 65 – 70 . London : Oxford University Press . This attitude is most fully articulated in the monumental volume of
- Landau , L. D. and Lifshitz , E. M. 1969 . Statistical Physics, , second edition , ix Reading, Mass. : Addison-Wesley . See p. 3 of Wightman's lecture cited in note 1; he refers specifically to a statement by “If one talks from the very beginning about the statistical distribution for small parts of a system (subsystems) and not for a closed system as a whole, then one avoids the whole question of the ergodic or similar hypotheses, which are not really essential for physical statistics.” See p. xi in the 1958