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

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Abstract

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.

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References

  1. Bokulich, A.: Reexamining the Quantum-Classical Relation: Beyond Reductionism and Pluralism. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  2. Chibbaro, S., Rondoni, L., Vulpiani, A.: Reductionism, Emergence and Levels of Reality. Springer, Berlin (2014)

    Book  Google Scholar 

  3. Berry, M.: Singular limits. Phys. Today 55, 10–11 (2002)

    Article  ADS  Google Scholar 

  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)

  5. Battermant, R.W.: The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction and Emergence. Oxford University Press, Oxford (2002)

    Google Scholar 

  6. Nagel, E.: The Structure of Science. Routledge, London (1961)

    Google Scholar 

  7. Berry, M.: Semi-classical mechanics in phase space: a study of wigner’s function. Philos. Trans. R. Soc. A. 287, 237–271 (1977)

    Article  ADS  MATH  Google Scholar 

  8. Berry, M.: Remarks on degeneracies of semiclassical energy levels. J. Phys. A 10, L193–L194 (1977)

    Article  ADS  Google Scholar 

  9. Berry, M.: Regular and irregular semiclassical wave functions. J. Phys. A 10, 2083–2091 (1977)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. Berry, M.V.: Exuberant interference: rainbows, tides, edges, (de)coherence. Philos. Trans. R. Soc. A 360, 1023–1037 (2002)

    Article  ADS  MATH  Google Scholar 

  11. Gibbs, J.W.: The Scientific Papers of J. Willard Gibbs, Vol. I Thermodynamics; Vol. II Misc. Dover, New York (1961)

    Google Scholar 

  12. Gibbs, J.W.: Elementary Principles in Statistical Mechanics. Charles Scribner’s Sons, New York (1902)

    MATH  Google Scholar 

  13. Gibbs, J.W.: Fourier’s series. Nature 59, 200 (1898)

    Article  ADS  Google Scholar 

  14. Gibbs, J.W.: Fourier’s series. Nature 59, 606 (1898)

    Article  ADS  Google Scholar 

  15. Wilbraham, H.: On a certain periodic function. Camb. Dublin Math. J. 3, 198–201 (1848)

    Google Scholar 

  16. Caldi, D.G., Mostow, D.G. (eds.) Proceedings of the Gibbs Symposium, Yale University, 17–18 May 1989, American Mathematics Society, AIP (1990)

  17. Jesseph, D.M.: The analyst. In: Grattan-Guinness, I., et al. (eds.) Landmark Writings in Western Mathematics, pp. 121–130. Elsevier, Amsterdam (2005)

    Chapter  Google Scholar 

  18. Hinch, E.J.: Perturbation Methods. Cambridge University Press, Cambridge (1991)

    Book  MATH  Google Scholar 

  19. Widom, B.: J. Chem. Phys. 43, 3892 (1965) (ibid p. 3896)

  20. Kadanoff, L.: Scaling laws for ising models near \(t_c\). Physics 2, 263 (1966)

    Google Scholar 

  21. Domb, C.: The Critical Point. Taylor and Francis, London (1996)

    Google Scholar 

  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. 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. Wheeler, L.P.: Josiah Willard Gibbs: The History of a Great Mind. Yale University Press, New Haven (1951)

    MATH  Google Scholar 

  25. Rukeyser, M.: Willard Gibbs: American Genius. Ox Bow Press, Woodbridge (1988)

    Google Scholar 

  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 

Download references

Acknowledgments

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.

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  1. The James Franck Institute, The University of Chicago, Chicago, IL, 60637, USA

    Leo P. Kadanoff

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  1. Leo P. Kadanoff
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Correspondence to Leo P. Kadanoff.

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Kadanoff, L.P. Reflections on Gibbs: From Statistical Physics to the Amistad V3.0. J Stat Phys 156, 1–9 (2014). https://doi.org/10.1007/s10955-014-1000-4

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