Abstract
The article begins with some personal comments by the author on the outstanding contributions of Michael Fisher to statistical mechanics and critical phenomena. Its major aim is to trace the contributions of a number of pioneering personalities to the early history of equilibrium statistical mechanics. Four different areas are considered: (1) Classical Statistical Mechanics, (2) Quantum Statistical Mechanics, (3) Interacting Systems, and (4) The Ising Model. The article is concerned with the development and applications of statistical mechanics when certain basic assumptions are made. It does not deal with the justification of these assumptions which is a sophisticated discipline of its own.
Similar content being viewed by others
REFERENCES
C. Domb, Physica A 177:1(1991).
K. G. Wilson, Nobel Lectures in Physics 1981–1990 (World Scientific), p. 100.
J. D. Watson, The Double Helix (Athaneum Press, 1968). Foreword by Sir Lawrence Bragg.
R. Clausius, Ann. Physik 100:353(1857),R. Clausius English translation, Phil. Mag. 14:108 (1859).
J. W. Gibbs, Proc. Am. Acad. 16:458(1889).
S. G. Brush, Statistical Physics and the Atomic Theory of Matter (Princeton University Press, 1983), p. 50.
C. H. D. Buys-Ballot, Ann. Phys. Leipzig 103:24D(1858).
R. Clausius, Ann. Physik 105:239(1858).
R. ClausiusEnglish translation, Phil. Mag. 17:81(1859).
Report of the Twenty-ninth Meeting of the British Association for the Advancement of Science (London, 1860), part 2:9. Reproduced in The Scientific Lectures and Papers of James Clerk Maxwell, P. M. Harman, ed. (Cambridge, 1990), pp. 615–616. The complete paper was published in Phil. Mag. January and June 1860. Maxwell's Scientific Papers, Vol. 1, p. 376.
Nature 8:437(1873);Maxwell's Scientific Papers, Vol. 2, p. 361.
S. G. Brush, Statistical Physics and the Atomic Theory of Matter (Princeton, 1983), p. 59. This book is a useful general reference for the material of this paper.
Lewis Campbell and William Garnett, The Life of James Clerk (Maxwell, London, 1882), p. 143(Reprinted Johnson Reprint Corporation, 1969).
Harvey S. Leff and Andrew F. Rex, eds., Maxwell's Demon (Adam Hilger, Bristol, 1990).
John Earman and John D. Norton, Stud. Hist. Phil. Mod. Phys. 29:435(1998)
John Earman and John D. Norton, Stud. Hist. Phil. Mod. Phys. 30:1(1999).
J. Maddox, Nature 345:109(1990).
N. Brown, New Scientist 35 (July 14, 1990).
Nature 15 (1876).
Maxwell's Scientific Papers, Vol. 2, p. 418.
A useful general reference is C. Cercignano, Ludwig Boltzmann, Oxford (1998).
It is interesting that this was already noted by Gibbs who wrote in Ref. 6 "In reading Clausius we seem to be reading mechanics; in reading Maxwell, and in much of Boltzmann's most valuable work, we seem rather to be reading in the theory of probabilities."
L. Boltzmann, Wien. Ber. 58:517(1868).
L. Boltzmann, Wien. Ber. 63:679(1871).
L. Boltzmann, Wien. Ber. 76:373(1877).
L. Boltzmann, Ann. Physik 60:392(1897).
English translation in S. G. Brush, Kinetic Theory (Pergamon Press, Oxford, 1966), Vol. 2, p. 238.
J. W. Gibbs, Elementary Principles in Statistical Mechanics (Scribner's, New York and Arnold, London, 1902).
Published as a book, E. Schrödinger, Statistical Thermodynamics (Cambridge, 1946).
A. Pais, Subtle is the Lord, The Science and Life of Einstein (American Philological Association, 1982), pp. 60–75.
The most comprehensive treatment in the literature is in L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, Oxford, 1958), Ch. 12.
A. Einstein, Ann. Phys. Leipzig 33:127(1910).
M. S. Smoluchowski, Ann. Phys. Leipzig 25:205(1908)
Phil. Mag. 23:165(1912).
M. Planck, Verh. D. Phys. Ges. 2:202(1900)
2:237(1900).
O. Lummer and E. Pringsheim, Verh. d. D. Phys. Ges. 1:23, 215 (1899).
Thomas S. Kuhn, Black-Body Theory and the Quantum Discontinuity 1894–1912 (Oxford, 1978).
Max Planck Theory of Heat (Macmillan, London, 1932).
Mark W. Zemansky, Heat and Thermodynamics, first edn. (McGraw-Hill, 1937).
A. B. Pippard, Classical Thermodynamics (Cambridge, 1957).
H. B. Callen, Thermodynamics (Wiley, 1960).
M. Planck, Ann. Phys. Lpz. 1:719(1900)
See ref. 32, pp. 144–152.
A. Einstein, Ann. d. Phys. 17:132(1905)
20:199(1906).
A. Einstein, Ann. d. Phys. 22:800(1907).
M. Planck, Ann. Phys. Lpz. 75:673(1924).
S. N. Bose, Z. Phys. 26:178(1924).
Reference 26, p. 246.
A. Einstein, Sitz. Preuss. Akad. Wiss., p. 261(1924)
A. Einstein, Sitz. Preuss. Akad. Wiss.p. 3(1925).
W. Pauli, Z. Phys. 31:765(1925).
E. Fermi, Z. Phys. 36:902(1926).
P. A. M. Dirac, Proc. Roy. Soc. A 112:661(1926).
P. A. M. Dirac, Quantum Mechanics, 4th edn. (Oxford, 1958).
C. G. Darwin and R. H. Fowler, Proc. Camb. Phil. Soc. 21:391(1922).
R. H. Fowler, Statistical Mechanics, first edn. (Cambridge, 1929).
R. H. Fowler, Statistical Mechanics, 2nd edn. (Cambridge, 1936).
R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics (Cambridge, 1939).
Reference 50, p. 30.
R. H. Fowler, Proc. Camb. Phil. Soc. 34:382(1938).
Reference 52, Chapter 6.
G. S. Rushbrooke, Introduction to Statistical Mechanics (Oxford, 1949).
C. Domb, The Critical Point (Taylor and Francis, London, 1996).
Reference 57, Chapter 2.
Reference 57, Chapter 3.
Reference 57, Chapter 4, pp. 101–112.
M. E. Fisher, J. Math. Phys. 5:944(1964).
Reference 57, Chapter 4, pp. 110–112.
Reference 57, Chapter 4, pp. 122–124.
The same development was suggested independently by J. Yvon, but his work was less well known.
Reference 57, Chapter 5, pp. 195–198.
See C. Domb, Chapter 1 in C. Domb and M. S. Green, Phase Transitions and Critical Phenomena, Vol. 3 (Academic Press, 1974) for a detailed discussion with references.
E. Ising, Z. Phys. 31:253(1925).
R. E. Peierls, Proc. Camb. Phil. Soc. 32:477(1936).
F. Cernuschi and H. Eyring, J. Chem. Phys. 7:547(1939).
H. A. Kramers and G. H. Wannier, Phys. Rev. 60:252, 263 (1941).
E. N. Lassettre and J. P. Howe, J. Chem. Phys. 9:747(1941).
E. W. Montroll, J. Chem. Phys. 9:706(1941).
C. Domb, Doctoral Thesis (Cambridge, 1949).
C. DombProc. Roy. Soc. A 196:36
C. DombProc. Roy. Soc. A 199:39(1949)
Reference 57, Chapter 5, p. 129–147.
J. E. Mayer and E. W. Montroll, J. Chem. Phys. 9:2(1941).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Domb, C. Some Observations on the Early History of Equilibrium Statistical Mechanics. Journal of Statistical Physics 110, 475–496 (2003). https://doi.org/10.1023/A:1022139230789
Issue date:
DOI: https://doi.org/10.1023/A:1022139230789
