The European Physical Journal Special Topics

, Volume 226, Issue 4, pp 539–549 | Cite as

A look back at the Ehrenfest classification

Translation and commentary of Ehrenfest's 1933 paper introducing the notion of phase transitions of different order
  • Tilman Sauer
Part of the following topical collections:
  1. Recent Advances in Phase Transitions and Critical Phenomena


A translation of Paul Ehrenfest's 1933 paper, entitled Phase transitions in the usual and generalized sense, classified according to the singularities of the thermodynamic potential is presented. Some historical commentary about the paper's context is also given.


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  1. 1.
    W. Janke, D.A. Johnston, R. Kenna, Nucl. Phys. B 736 [FS], 319 (2006)ADSCrossRefGoogle Scholar
  2. 2.
    P. Ehrenfest, Phasenumwandlungen im ueblichen und erweiterten Sinn, classifiziert nach den entsprechenden Singularitaeten des thermodynamischen Potentiales, Proc. Royal Acad. Amsterdam 36, 153 (1933) (Commun. Kamerlingh Onnes Inst. Leiden, Suppl. 75b)zbMATHGoogle Scholar
  3. 3.
    G. Jaeger, Arch. Hist. Ex. Sci. 53, 51 (1998)CrossRefGoogle Scholar
  4. 4.
    S.G. Brush, The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century (North-Holland, Amsterdam, 1976)Google Scholar
  5. 5.
    J.S. Rowlinson, Nature 224, 541 (1969)ADSCrossRefGoogle Scholar
  6. 6.
    M.J. Klein et al. (eds), The Collected Papers of Albert Einstein. The Swiss Years: Writings, 1909–1911 (Princeton University Press, 1993), Vol. 3, pp. 283–312Google Scholar
  7. 7.
    M. Niss, Arch. Hist. Ex. Sci. 59, 267 (2005)MathSciNetCrossRefGoogle Scholar
  8. 8.
    P.F. Dahl, Superconductivity. Its Historical Roots and Development from Mercury to the Ceramic Oxides (American Institute of Physics, New York, 1992)Google Scholar
  9. 9.
    J. Matricon, G. Waysand. The Cold Wars. A History of Superconductivity (Rutgers University Press, New Brunswick, NJ, 2003)Google Scholar
  10. 10.
    W.H. Keesom, Proc. Royal Acad. Amsterdam 36, 147 (1932) (Commun. Kamerlingh Onnes Inst. Leiden. Suppl. 75a)Google Scholar
  11. 11.
    W.H. Keesom, K. Clusius, Proc. Royal Acad. Amsterdam 35, 307 (1932) (Commun. Kamerlingh Onnes Inst. 219e)Google Scholar
  12. 12.
    W.H. Keesom, A.P. Keesom, Proc. Royal Acad. Amsterdam 35, 736 (1932) (Commun. Kamerlingh Onnes Inst. 221d)Google Scholar
  13. 13.
    J.A. Lipa, J.A. Nissen, D.A. Stricker, D.R. Swanson, T.C.P. Chui, Phys. Rev. B 68, 174518 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    P. Kapitza, Nature 141, 74 (1938)ADSCrossRefGoogle Scholar
  15. 15.
    J.F. Allen, A.D. Misener, Nature 142, 643 (1938)ADSCrossRefGoogle Scholar
  16. 16.
    M.J. Klein, The Making of a Theoretical Physicist (North-Holland, Amsterdam, 1972)Google Scholar
  17. 17.
    P. Ehrenfest, T. Ehrenfest, Begriffliche Grundlagen der statistischen Auffassung in der Mechanik, in Encyclopädie der mathematischen Wissenschaften mit Einschluß ihrer Anwendungen, Band IV, 2. Teil, F. Klein, C. Müller (eds.) (Teubner, Leipzig, 1911), pp. 3–90Google Scholar
  18. 18.
    P. Ehrenfest, T. Ehrenfest, The Conceptual Foundations of the Statistical Approach in Mechanics (Cornell University Press, New York, 1959)Google Scholar
  19. 19.
    E. Pèrez, B. Pié i Valls, Eur. Phys. J. H 41, 93 (2016)CrossRefGoogle Scholar
  20. 20.
    H. Schmidt-Böcking, L. Schmidt, H.J. Lüdde, W. Trageser, A. Templeton, T. Sauer, Eur. Phys. J. H 41, 327 (2016)CrossRefGoogle Scholar
  21. 21.
    I. Unna, T. Sauer, Ann. Phys. 525, A15 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    M. Schneider, Zwischen zwei Disziplinen. B.L. van der Waerden und die Entwicklung der Quantenmechanik (Springer, Heidelberg, 2011)Google Scholar
  23. 23.
    A. Einstein, Nachruf Paul Ehrenfest, Almanak van het Leidsche Studencorps (Doesburg, Leiden, 1934). English Translation in: Out of my later years (Philosophical Library, New York, 1950), pp. 236–239Google Scholar
  24. 24.
    W.H. Keesom, K. Clusius, Proc. Royal Acad. Amsterdam 34, 605 (1931) (Commun. Kamerlingh Onnes Inst. Leiden 216b)Google Scholar
  25. 25.
    J.W. Gibbs, Transactions of the Connecticut Academy of Arts and Sciences II (1873) 309–342, 383–404Google Scholar
  26. 26.
    F. Simon, Ann. Phys. 68, 241 (1922)CrossRefGoogle Scholar
  27. 27.
    F. Simon, Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin). Physikalisch-mathematische Klasse 477 (1926)Google Scholar

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© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Institute of Mathematics, Johannes Gutenberg UniversityMainzGermany

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