Summary
Many historians of science recognize that the outcome of the celebrated debate on Boltzmann's H-Theorem, which took place in the weekly scientific journal Nature, beginning at the end of 1894 and continuing throughout most of 1895, was the recognition of the statistical hypothesis in the proof of the theorem. This hypothesis is the Stosszahlansatz or “hypothesis about the number of collisions.” During the debate, the Stosszahlansatz was identified with another statistical hypothesis, which appeared in Proposition II of Maxwell's 1860 paper; Burbury called it Condition A. Later in the debate, Bryan gave a clear formulation of the Stosszahlansatz. However, the two hypotheses are prima facie different. Burbury interchanged them without justification or even warning his readers. This point deserves clarification, since it touches upon subtle questions related to the foundation of the theory of heat. A careful reading of the arguments presented by Burbury and Bryan in their various invocations of both hypotheses can clarify this technical point. The Stosszahlansatz can be understood in terms of geometrical invariances of the problem of a collision between two spheres. A byproduct of my analysis is a clarification of the debate itself, which is apparently obscure.
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References
Boltzmann, L. (1872) “Further Studies on the Thermal Equilibrium of Gas Molecules,” translated in S. G. Brush (1965, 1966, 1972), vol. 2, pp. 88–175.
Boltzmann, L. (1877) “On the relation of a General Mechanical Theorem on the Second Law of Thermodynamics,” translated in S. G. Brush (1965, 1966, 1972), vol. 2, pp. 188–202.
Boltzmann, L. (1895a) “On certain questions of the Theory of Gases,” Nature, 51, p. 413.
Boltzmann, L. (1895b) “On the Minimum Theorem in the Theory of Gases,” Nature, 52, p. 221.
Boltzmann, L. (1896) Lectures on Gas Theory, translated by S. G. Brush, University of California Press, Berkeley and Los Angeles, 1964.
Brush, S. G. (ed) (1965, 1966, 1972) Kinetic Theory, 3 vols, Pergamon Press, Oxford.
Brush, S. G. (1976) The Kind of Motion We Call Heat, 2 vols., North-Holland, Amsterdam.
Bryan, G. H. (1891) “Researches Related to the connection of the Second Law with Dynamical Principles,” British Association Report, 61, pp. 85–122.
Bryan, G. H. (1894a) “Report on the Present State of our Knowledge of Thermodynamics,” British Association Report, 64, pp. 64–106.
Bryan, G. H. (1894b) “The Kinetic Theory of Gases,” Nature, 51, p. 176.
Bryan, G. H. (1895) “The Assumption in Boltzmann's Minimum Theorem,” Nature, 52, pp. 29–30.
Burbury, S. H. (1886) “The Foundations of the Kinetic Theory of Gases,” Philosophical Magazine, [5], 21, pp. 481–483.
Burbury, S. H. (1890) “On some Problems in the Kinetic Theory of Gases,” Philosophical Magazine, [5], 30, pp. 298–317.
Burbury, S. H. (1891) “On the Collision of Elastic Bodies,” Abstract, Proceedings of the Royal Society of London, 50, pp. 175–179.
Burbury, S. H. (1892) “On the Collision of Elastic Bodies,” Philosophical Transactions, 183 A, pp. 407–422.
Burbury, S. H. (1894a) “Boltzmann's Minimum Function,” Nature, 51, p. 78–79.
Burbury, S. H. (1894b) “The Kinetic Theory of Gases,” Nature, 51, pp. 175–176.
Burbury, S. H. (1895a) “Boltzmann's Miminum Function,” Nature, 51, p. 320.
Burbury, S. H. (1895b) “Boltzmann's Minimum Function,” Nature, 52, pp. 104–105.
Burbury, S. H. (1904) “On the Theory of Diminishing Entropy,” Philosophical Magazine, [6], 8, pp. 43–49.
Cercignani, C. (1972) “On the Boltzmann Equation for Rigid Spheres,” Transport Theory and Statistical Physics, 2, p. 211–225.
Clausius, R. E. J. (1858) “On the mean lengths of the paths described by the separate molecules of gaseous bodies,” translated by F. Guthrie (1859), republished in S. G. Brush (1965, 1966, 1972), vol. 1, pp. 135–147.
Clausius, R. E. J. (1862) “On the conduction of Heat by Gases,” translated by G. C. Foster (1862) in Philosophical Magazine, [4], 23, pp. 417–435, 512–534.
Culverwell, E. P. (1894a) “Dr. Watson's Proof of Boltzmann's Theorem on Permanence of Distributions,” Nature, 50, p. 617.
Culverwell, E. P. (1894b) “Boltzmann's Minimum Theorem,” Nature, 51, p. 105.
Culverwell, E. P. (1895a) “Boltzmann's Minimum Theorem,” Nature, 51, p. 246.
Culverwell, E. P. (1895b) “Professor Boltzmann's letter on the kinetic theory of Gases,” Nature, 51, p. 581.
Ehrenfest, P. and Ehrenfest T. (1911) The Conceptual Foundations of Statistical Mechanics, translated by M. J. Moravcsik, Cornell University Press, republished by Dover, New York, 1958.
Grad, H. (1958) “Principles of the Kinetic Theory of Gases,” in S. Flügge (ed.), Thermodynamics of Gases, Encyclopaedia of Physics, vol. XII, Springer-Verlag, Berlin, pp. 205–294.
Harris, Stewart (1971) An Introduction to the Theory of the Boltzmann Equation, Holt, Rinehart and Winston, New York.
Klein, M. J. (1973) “The Development of Boltzmnann's Statistical Ideas,” in E. G. D. Cohen & W. Thirring (eds) The Boltzmann Equation: Theory and Applications, Springer-Verlag, Berlin, pp. 53–105.
Kuhn, T. S. (1978) Black-body Theory and the Quantum Discontinuity 1894–1912, Oxford.
Lanford III, O. E. (1975) “Time Evolution of Large Classical Systems,” in J. Moser (ed.) Dynamical Systems, Theory and Applications, Lecture Notes in Physics, 38, Springer-Verlag, Berlin, pp. 1–111.
Maxwell, J. C. (1860) “Illustrations of the Dynamical Theory of Gases,” Philosophical Magazine, [4], 19, pp. 19–32, 20, pp. 21–37. Republished in W. D. Niven (ed.) (1890), vol. 1, pp. 377–409. Also republished in part in S. G. Brush (ed) (1965, 1966, 1972), vol. 1, pp. 148–178.
Maxwell, J. C. (1866) “On the Dynamical Theory of Gases,” Philosophical Transactions of the Royal Society of London, 157, pp. 49–88. Reprinted in W. D. Niven (ed.) (1890), vol. 2, pp. 26–78. Also reprinted in S. G. Brush (ed.) (1965, 1966, 1972), vol. 2. pp. 23–87.
Niven, W. D. (1890) The Scientific Papers of James Clerk Maxwell, 2 vols, Cambridge University Press; republished by Dover, New York, 1961.
Truesdell, C. A. & Muncaster, R. G. (1979) Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas (Treated as a Branch of Rational Mechanics), Academic Press, New York.
Watson, H. W. (1876) A Treatise on the Kinetic Theory of Gases, First Edition, Clarendon, Oxford.
Watson, H. W. (1893) A Treatise on the Kinetic Theory of Gases, Second Edition, Clarendon, Oxford.
Watson, H. W. (1894) “Boltzmann's Minimum Theorem,” Nature, 51, p. 105.
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Communicated by R. H. Stuewer
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Dias, P.M.C. “Will someone say exactly what the H-theorem proves?” A study of Burbury's Condition A and Maxwell's Proposition II. Arch. Hist. Exact Sci. 46, 341–366 (1994). https://doi.org/10.1007/BF00375640
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DOI: https://doi.org/10.1007/BF00375640