Journal of Statistical Physics

, Volume 156, Issue 1, pp 1–9 | Cite as

Reflections on Gibbs: From Statistical Physics to the Amistad V3.0

  • Leo P. Kadanoff


This note is based upon a talk given at an APS meeting in celebration of the achievements of J. Willard Gibbs. J. Willard Gibbs, the younger, was the first American physical sciences theorist. He was one of the inventors of statistical physics. He introduced and developed the concepts of phase space, phase transitions, and thermodynamic surfaces in a remarkably correct and elegant manner. These three concepts form the basis of different areas of physics. The connection among these areas has been a subject of deep reflection from Gibbs’ time to our own. This talk therefore celebrated Gibbs by describing modern ideas about how different parts of physics fit together. I finished with a more personal note. Our own J. Willard Gibbs had all his many achievements concentrated in science. His father, also J. Willard Gibbs, also a Professor at Yale, had one great non-academic achievement that remains unmatched in our day. I describe it.


Philosophy of science History of science Statistical physics 



I have had useful discussions about this work with Michael Fisher, Steve Berry, Marko Kleine Berkenbusch, Robert Batterman, and Michael Berry. I am indebted to Amy Kolan and her senior class at St. Olaf for helpful critical comments. Research supported in part by NSF-DMR and also by the University of Chicago MRSEC and NSF grant number DMR-0820054.


  1. 1.
    Bokulich, A.: Reexamining the Quantum-Classical Relation: Beyond Reductionism and Pluralism. Cambridge University Press, Cambridge (2008)CrossRefGoogle Scholar
  2. 2.
    Chibbaro, S., Rondoni, L., Vulpiani, A.: Reductionism, Emergence and Levels of Reality. Springer, Berlin (2014)CrossRefGoogle Scholar
  3. 3.
    Berry, M.: Singular limits. Phys. Today 55, 10–11 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    Berry, M.: Asymptotics, singularities and the reduction of theories. In: Prawitz, D., Skyrms, B., Westerstaahl, D. (eds.) Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science, pp. 597–607 (1994)Google Scholar
  5. 5.
    Battermant, R.W.: The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction and Emergence. Oxford University Press, Oxford (2002)Google Scholar
  6. 6.
    Nagel, E.: The Structure of Science. Routledge, London (1961)Google Scholar
  7. 7.
    Berry, M.: Semi-classical mechanics in phase space: a study of wigner’s function. Philos. Trans. R. Soc. A. 287, 237–271 (1977)ADSCrossRefMATHGoogle Scholar
  8. 8.
    Berry, M.: Remarks on degeneracies of semiclassical energy levels. J. Phys. A 10, L193–L194 (1977)ADSCrossRefGoogle Scholar
  9. 9.
    Berry, M.: Regular and irregular semiclassical wave functions. J. Phys. A 10, 2083–2091 (1977)ADSCrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Berry, M.V.: Exuberant interference: rainbows, tides, edges, (de)coherence. Philos. Trans. R. Soc. A 360, 1023–1037 (2002)ADSCrossRefMATHGoogle Scholar
  11. 11.
    Gibbs, J.W.: The Scientific Papers of J. Willard Gibbs, Vol. I Thermodynamics; Vol. II Misc. Dover, New York (1961)Google Scholar
  12. 12.
    Gibbs, J.W.: Elementary Principles in Statistical Mechanics. Charles Scribner’s Sons, New York (1902)MATHGoogle Scholar
  13. 13.
    Gibbs, J.W.: Fourier’s series. Nature 59, 200 (1898)ADSCrossRefGoogle Scholar
  14. 14.
    Gibbs, J.W.: Fourier’s series. Nature 59, 606 (1898)ADSCrossRefGoogle Scholar
  15. 15.
    Wilbraham, H.: On a certain periodic function. Camb. Dublin Math. J. 3, 198–201 (1848)Google Scholar
  16. 16.
    Caldi, D.G., Mostow, D.G. (eds.) Proceedings of the Gibbs Symposium, Yale University, 17–18 May 1989, American Mathematics Society, AIP (1990)Google Scholar
  17. 17.
    Jesseph, D.M.: The analyst. In: Grattan-Guinness, I., et al. (eds.) Landmark Writings in Western Mathematics, pp. 121–130. Elsevier, Amsterdam (2005)CrossRefGoogle Scholar
  18. 18.
    Hinch, E.J.: Perturbation Methods. Cambridge University Press, Cambridge (1991)CrossRefMATHGoogle Scholar
  19. 19.
    Widom, B.: J. Chem. Phys. 43, 3892 (1965) (ibid p. 3896)Google Scholar
  20. 20.
    Kadanoff, L.: Scaling laws for ising models near \(t_c\). Physics 2, 263 (1966)Google Scholar
  21. 21.
    Domb, C.: The Critical Point. Taylor and Francis, London (1996)Google Scholar
  22. 22.
    Stokes, G.G.: On the numerical calculation of a class of definite integrals and infinite series. Trans. Camb. Philos. Soc. IX(1), 166–189 (1847)Google Scholar
  23. 23.
    Stokes, G.G.: On the discontinuity of arbitrary constants which appear in divergent developments. Trans. Camb. Philos. Soc. X(2), 105–128 (1848)Google Scholar
  24. 24.
    Wheeler, L.P.: Josiah Willard Gibbs: The History of a Great Mind. Yale University Press, New Haven (1951)MATHGoogle Scholar
  25. 25.
    Rukeyser, M.: Willard Gibbs: American Genius. Ox Bow Press, Woodbridge (1988)Google Scholar
  26. 26.
    Jones, H.: Mutiny on the Amistad: The Saga of a Slave Revolt and Its Impact on American Abolition, Law, and Diplomacy. Oxford University Press, New York (1987)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.The James Franck InstituteThe University of ChicagoChicagoUSA

Personalised recommendations