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The Thought Experiment of Maxwell’s Demon and the Origin of Irreversibility

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Abstract

The problem of the irreversibility’s origin in thermodynamic processes occupies a distinguished place among many and lasting attempts by researchers to derive irreversibility from molecular-mechanical principles. However, this problem is still open and no universally accepted solution may be given during any course. In this paper, I shall try to show that the examining of Maxwell’s demon thought experiment may provide insight into the difficulties that emerge, looking for this origin because: (i) it is connected with the notion of irreversibility, and (ii) one of its functions is that of the “reversibility objection.” In order to illustrate this point, I study Boltzmann’s approach to the problem of a molecular-mechanical interpretation of irreversibility and I show that an auxiliary assumption (the selected direction of time) is responsible for producing irreversibility. But this result is accordant with the predictions of Maxwell’s demon thought experiment: the assumptions of this kind are not dictated by molecular-mechanical principles but are separate input in the model-systems used.

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Notes

  1. The term “heat-death” was introduced by Hermann von Helmholtz, who elaborated the consequences of Thomson’s Principle of Dissipation and, two years later, described the “heat-death” of the universe, the consequence of the transformation of all energy into internal energy (Tyndall and Francis 1966, p. 114).

  2. According to the molecular hypothesis, mass consists of individual particles (is not continuous). According to the mechanical hypothesis, the behavior of the individual particles is defined only by the dynamics and kinetics of Newton’s deterministic mechanics.

References

  • Ageno, M. (1992). Le Origini della Irreversibilitá. Turin: Bollati Boringhieri.

    Google Scholar 

  • Arkeryd, L. (1981). On the Boltzmann’s equation I and II. Archive for Rational Mechanics and Analysis, 45, 1–34.

    Article  Google Scholar 

  • Batterman, R. W. (1991). Randomness and probability in dynamical theories: On the proposals of the Prigogine School. Philosophy of Science, 58, 241–263.

    Article  Google Scholar 

  • Boltzmann, L. (1872). Weitere Studien Über das Wärmegleichgewicht unter Gasmolekülen. Wiener Berichte, 66, 275–370.

    Google Scholar 

  • Bricmont, J. (1996). Science of Chaos or Chaos of science. In P. R. Gross, N. Levitt, & M. W. Lewis (Eds.), The flight from science and reason (pp. 131–175). New York: New York Academy of Sciences.

    Google Scholar 

  • Bricmont, J. (2001). Bayes, Boltzmann and Bohm: Probabilities in physics. In J. Bricmont et al. (Eds.), Chance in physics: Foundations and perspectives (pp. 3–21). Berlin: Springer-Verlag.

    Chapter  Google Scholar 

  • Brown, H. R., & Uffink, J. (2001). The origins of time-asymmetry in thermodynamics: The Minus first law. Studies in History and Philosophy of Modern Physics, 32(4), 525–538.

    Article  Google Scholar 

  • Cercignani, C. (1977). The Boltzmann equation and its applications. New York: Springer-Verlag.

    Google Scholar 

  • Cercignani, C. (1998). Ludwig Boltzmann, the man who trusted atoms. Oxford: Oxford University Press.

    Google Scholar 

  • Cercignani, C., Illner, R., & Pulvirenti, M. (1994). The mathematical theory of dilute gases. New York: Springer-Verlag.

    Google Scholar 

  • Cercignani, C., & Lampis, M. (1981). On the H-theorem for polyatomic gases. Journal of Statistical Physics, 26, 795–801.

    Article  Google Scholar 

  • Coveney, R., & Highfield, R. (1990). The arrow of time-a voyage through science to solve time’s greatest mystery. London: W. H. Allen.

    Google Scholar 

  • Daub, E. (1970). Maxwell’s demon. Studies in History and Philosophy of Science, 1, 213–227.

    Article  Google Scholar 

  • Di Perma, R., & Lions, P. L. (1989). On the cauchy problem for Boltzmann equations: Global existence and weak stability. Annals of Mathematics, 130, 321–336.

    Article  Google Scholar 

  • Goldstein, S. (2001). Boltzmann’s approach to statistical mechanics. In J. Bricmont et al. (Eds.), Chance in physics: Foundations and perspectives (pp. 39–54). Berlin: Springer-Verlag.

    Chapter  Google Scholar 

  • Harman, P. M. (1990). The scientific letters and papers of James Clerk Maxwell (Vol. 1). Cambridge: Cambridge University Press.

    Google Scholar 

  • Illner, R., & Pulvirenti, M. (1986). Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum. Communications in Mathematical Physics, 105, 189–203.

    Article  Google Scholar 

  • Illner, R., & Pulvirenti, M. (1989). Global validity of the Boltzmann equation for two- and three-dimensional rare gas in vacuum. Communications in Mathematical Physics, 121, 143–146.

    Article  Google Scholar 

  • Illner, R., & Shinbrot, M. (1984). The Boltzmann equation: Global existence for a rare gas in an infinite vacuum. Communications in Mathematical Physics, 95, 217–226.

    Article  Google Scholar 

  • Jaynes, E. T. (1971). Violation of Boltzmann’s H-theorem in real gases. Physical Review A, 4, 747–750.

    Article  Google Scholar 

  • Klein, M. J. (1973). The development of Boltzmann’s statistical ideas. In E. G. D. Cohen & W. Thirring (Eds.), The Boltzmann equation. Theory and application (pp. 53–106). Vienna: Springer-Verlag.

    Google Scholar 

  • Lanford, O. E. (1975). Time evolution of large classical systems. In J. Moser (Ed.), Dynamical systems, theory and applications (Vol. 38, pp. 1–111). Berlin: Springer-Verlag.

    Chapter  Google Scholar 

  • Lebowitz, J. L. (1993). Boltzmann’s entropy and time’s arrow. Physics Today, 46, 32–38.

    Article  Google Scholar 

  • Leff, H. S., & Rex, A. F. (2003a). Maxwell’s Demon and the second law. In D. Sheehan (Ed.), First international conference on quantum limits to the second law (pp. 408–419). New York: American Institute of Physics.

    Google Scholar 

  • Leff, H. S., & Rex, A. F. (2003b). Maxwell’s Demon 2: Entropy, classical and quantum information, computing. Bristol: IOP.

    Google Scholar 

  • Loschmidt, J. (1876). Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht aut die Schwerkraft. Wiener Berichte, 73, 128–142.

    Google Scholar 

  • Maxwell, J. C. (1855). Letter to W. Thomson, 15 May 1855. Proceedings of the Cambridge Philosophical Society 1936, 32, 695–750.

  • Maxwell, J. C. (1867). Letter to P. G. Tait, 11 December 1867. In C. G. Knott (Ed.), Life and scientific work of Peter Guthrie Tait (pp. 213–214). Cambridge: Cambridge University Press, 1911.

  • Maxwell, J. C. (1868). Letter to M. Pattison, April 1868. In P. M. Harman (Ed.), The scientific letters and papers of James Clerk Maxwell (Vol. 2, pp. 366–367). Cambridge: Cambridge University Press, 1990.

  • Maxwell, J. C. (1870). Letter to J. W. Strutt, 6 December 1870. In R. J. Strutt (Ed.), Life of John William Strutt, Third Baron Rayleigh (pp. 47–48). Madison/Wisconsin: University of Wisconsin Press, 1968.

  • Maxwell, J. C. (1871). Theory of heat. London: Longmans, Green & Co.

    Google Scholar 

  • Maxwell, J. C. (1873). Letter to P. G. Tait, 1 December 1873. In E. Garber, S. G. Brush, & C. W. F. Everitt (Eds.), Maxwell on heat and statistical mechanics (pp. 223–226). Cambridge, MA: MIT Press, 1995.

  • Maxwell, J. C. (1878a). Diffusion. Encyclopedia Britannica (9th Ed., pp. 214–221). Chicago: Encyclopedia Britannica, Inc.

    Google Scholar 

  • Maxwell, J. C. (1878b). Tait’s thermodynamics. Nature, 17, 257–259, 278–280.

    Google Scholar 

  • Maxwell, J. C. (Undated). Undated Letter to P. G. Tait. In C. G. Knott (Ed.), Life and scientific work of Peter Guthrie Tait (pp. 214–215). London: Cambridge University Press, 1911.

  • Nishida, T. & Imai, K. (1976). Global solutions to the initial value problem for the nonlinear Boltzmann equation. In Publications of the Research Institute for Mathematical Sciences (Vol. 12, pp. 229–239). Kyoto: Kyoto University.

  • Price, H. (1996). Time’s arrow and Archimedes’ point. New York: Oxford University Press.

    Google Scholar 

  • Price, H. (1997). Time symmetry in microphysics. Philosophy of science, supplement. Proceedings of the 1996 Biennial Meetings of Philosophy of Science Association, 64, S235–S244.

  • Prigogine, I., & Stengers, I. (1979). La Nouvelle Alliance. Metamorphoses de la Science. Paris: Gallimard.

    Google Scholar 

  • Prigogine, I., & Stengers., I. (1988). Entre le Temps et l’ Eternité. Paris: Fayard.

    Google Scholar 

  • Shizuta, Y., & Asano, K. (1974). Global solutions of the Boltzmann equation in a bounded convex domain. Proceedings of the Japan Academy, 53, 3–5.

    Google Scholar 

  • Spohn H. (2001). Microscopic time reversibility and the Boltzmann equation. In J. Bricmont et al. (Eds.), Chance in physics: Foundations and perspectives (pp. 55–59). Berlin: Springer-Verlag.

    Chapter  Google Scholar 

  • Thomson, W. (1852). On the universal tendency in nature to the dissipation of mechanical energy. Philosophical Magazine, 4, 304–306.

    Google Scholar 

  • Thomson, W. (1874). The kinetic theory of the dissipation of energy. Nature, 9, 441–444.

    Article  Google Scholar 

  • Thomson, W. (1879). The sorting Demon of Maxwell. Proceedings Royal Society of London, 9, 113–114.

    Google Scholar 

  • Tyndall, J. & Francis, W. (1966). Scientific Memoirs, Natural Philosophy. London: Taylor and Francis.

    Google Scholar 

  • Uffink, J. (2001). Bluff your way in the second law of thermodynamics. Studies in History and Philosophy of Modern Physics, 32(3), 305–394.

    Article  Google Scholar 

  • Ukai, S. (1974). On the existence of global solutions of mixed problem for non-linear Boltzmann equation. Proceedings of the Japan Academy, 50, 179–184.

    Article  Google Scholar 

  • Van Kampen, N. G. (1962). Statistical mechanics of irreversible processes. In E. G. D. Cohen (Ed.), Fundamental problems in statistical mechanics. Amsterdam: North-Holland Publishing Co.

    Google Scholar 

  • Zermelo, E. (1896). Über Einen Satz der Dynamik und die Mechanische Wärme-Theorie. Wiedemann’s Annalen, 57, 485–494.

    Google Scholar 

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Correspondence to Aspasia S. Moue.

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Moue, A.S. The Thought Experiment of Maxwell’s Demon and the Origin of Irreversibility. J Gen Philos Sci 39, 69–84 (2008). https://doi.org/10.1007/s10838-008-9061-1

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