Why Typicality Does Not Explain the Approach to Equilibrium

  • Roman FriggEmail author
Part of the Synthese Library book series (SYLI, volume 347)


Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions.


Lebesgue Measure Statistical Mechanic Invariant Measure Measure Zero High Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Special thanks goes to David Lavis for many illuminating discussions on SM in general, and the Boltzmannian approach in particular. I also would like to thank Craig Callender, Stephan Hartmann, Carl Hoefer, Wolfgang Pietsch, Charlotte Werndl, and two anonymous referees for valuable comments on earlier drafts. Thanks to Jean Bricmont for a helpful email conversation on his mixing condition discussed in Section 4.3, and to Detlef Dürr for drawing my attention to omissions in my first bibliography. Many thanks to Flavia Padovani for helping me with those passages in Zanghì’s chapter that were beyond the reach of my ‘FAPP Italian’. Thanks to Mauricio Suárez for organising the workshop at which this paper has first been presented, and thanks to the audiences in Madrid and Oxford for stimulating discussions. Finally, I would like to acknowledge financial support from two project grants of the Spanish Ministry of Science and Education (SB2005-0167 and HUM2005-04369).


  1. Albert, D. (2000), Time and Chance, Cambridge, MA: Harvard University Press.Google Scholar
  2. Arnold, V. I. (2006), Ordinary Differential Equations. Heidelberg: Springer.Google Scholar
  3. Boltzmann, L. (1877), ‘Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung resp. den Sätzen über das Wärmegleichgewicht. Wiener Berichte 76, 373-435. Reprinted in F. Hasenöhrl (ed.): Wissenschaftliche Abhandlungen. Leipzig: J. A. Barth 1909, Vol. 2, 164-223.Google Scholar
  4. Bricmont, J. (1996), Science of Chaos or Chaos in science?, In P. R. Gross, N. Levitt, and M. W. Lewis (eds.), The Flight from Science and Reason, Annals of the New York Academy of Sciences, New York, NY Vol. 775, 131-175.Google Scholar
  5. Bricmont, J. (2001), Bayes, Boltzmann and Bohm: Probabilities in physics, in Bricmont et al., 3–21.Google Scholar
  6. Callender, C. (1999), Reducing thermodynamics to statistical mechanics: The case of entropy, Journal of Philosophy 96, 348–373.CrossRefGoogle Scholar
  7. Callender, C. (2001), Taking thermodynamics too seriously, Studies in the History and Philosophy of Modern Physics 32, 539–53.CrossRefGoogle Scholar
  8. Callender, C. (2010), The past hypothesis meets gravity, forthcoming In G. Ernst and A. Hüttemann (eds.), Time, Chance and Reduction. Philosophical Aspects of Statistical Mechanics. Cambridge: Cambridge University Press 2010, pp. 34–58.Google Scholar
  9. Dürr, D. (1998), Über den Zufall in der Physik, manuscript presented at the 1998 Leopoldina Meeting in Halle. Available at
  10. Dürr, D. (2001), Bohmsche Mechanik als Grundlage der Quantenmechanik. Berlin: Springer.Google Scholar
  11. Dürr, D., S. Goldsein and N. Zanghì (1992), Quantum Equilibrium and the Origin of Absolute Uncertainty, Journal of Statistical Physics 67, 843–907.CrossRefGoogle Scholar
  12. Earman, J. (2006), The “past hypothesis”: Not even False, Studies in History and Philosophy of Modern Physics 37, 399–430.CrossRefGoogle Scholar
  13. Earman, J. and Rédei, M. (1996), Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics, British Journal for the Philosophy of Science 47, 63–78.CrossRefGoogle Scholar
  14. Ehrenfest, P. and Ehrenfest-Afanassjewa, T. (1912/1959), The Conceptual Foundations of the Statistical Approach in Mechanics. New York NY: Dover 2002. (First published in German in 1912; first English Translation 1959.)Google Scholar
  15. Frigg, R. (2008), A Field Guide to Recent Work on the Foundations of Statistical Mechanics, In Rickles, D. (ed.), The Ashgate Companion to Contemporary Philosophy of Physics. London: Ashgate, 99–196.Google Scholar
  16. Galvan, B. (2006), Typicality vs. probability in trajectory-based formulations of quantum mechanics, Foundations of Physics 37, 1540–1562.CrossRefGoogle Scholar
  17. Goldstein, S. (2001), Boltzmann’s Approach to Statistical Mechanics, in: Bricmont et al. 2001, 39–54.Google Scholar
  18. Goldstein, S. and Lebowitz, J. L. (2004), On the (Boltzmann) entropy of non-equilibrium systems, Physica D 193, 53–66.Google Scholar
  19. Goldstein, S., Lebowitz, J. L. Tomulka, R. and Zanghì, N. (2006), Canonical Typicality, Physical Review Letters 96, Issue 5.Google Scholar
  20. Hitchcock, C. (ed.) (2004) Contemporary Debates in Philosophy of Science. Malden, MA: Blackwell.Google Scholar
  21. Lavis, D. (2005), Boltzmann and Gibbs: An attempted reconciliation, Studies in History and Philosophy of Modern Physics 36, 245–273.CrossRefGoogle Scholar
  22. Lavis, D. (2008), Boltzmann, Gibbs and the concept of equilibrium, forthcoming in Philosophy of Science, 75 (December 2008), pp. 682–696.Google Scholar
  23. Lebowitz, J. L. (1993a), Boltzmann’s entropy and time’s arrow, Physics Today, September Issue, 32–38.Google Scholar
  24. Lebowitz, J. L. (1993b), Macroscopic laws, microscopic dynamics, time’s arrow and Boltzmann’s entropy, Physica A 194, 1–27.Google Scholar
  25. Lebowitz, J. L. (1999), Statistical mechanics: A selective review of two central issues, Reviews of Modern Physics 71, 346–357.CrossRefGoogle Scholar
  26. Loewer, B. (2001), Determinism and chance, Studies in History and Philosophy of Modern Physics 32, 609–629.Google Scholar
  27. Malament, D. B. and Zabell, S. L. (1980), Why Gibbs phase averages work, Philosophy of Science 47, 339–349.CrossRefGoogle Scholar
  28. Maudlin, T. (2007), What could be objective about probabilities?, Studies in History and Philosophy of Modern Physics 38, 275–291.CrossRefGoogle Scholar
  29. Penrose, R. (1989), The Emperor’s New Mind. Oxford: Oxford University Press.Google Scholar
  30. Salmon, W. (1992), Scientific Explanation, In M. Salmon, et al. (eds.), Introduction to the Philosophy of Science. Cambridge: Hackett, 7–23.Google Scholar
  31. Sklar, L. (1973), Statistical explanation and ergodic theory, Philosophy of Science 40, 194–212.CrossRefGoogle Scholar
  32. Sklar, L. (1993), Physics and Chance. Philosophical Issues in the Foundations of Statistical Mechanics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  33. Uffink, J. (2007), Compendium of the foundations of classical statistical physics, In J. Butterfield and J. Earman (eds.), Philosophy of Physics. Amsterdam: North Holland, 923–1047.CrossRefGoogle Scholar
  34. van Lith, J. (2001), Ergodic theory, interpretations of probability and the foundations of statistical mechanics, Studies in History and Philosophy of Modern Physics 32, 581–594.CrossRefGoogle Scholar
  35. Volchan, S. B. (2007), Probability as Typicality, Studies in History and Philosophy of Modern Physics 38, 801–814.CrossRefGoogle Scholar
  36. Zanghì, N. (2005), I Fondamenti concettuali dell’approccio statistico in Fisica, In V. Allori, M. Dorato, F. Laudisa and N. Zanghì (eds.), La Natura Delle Cose. Introduzione ai Fundamenti e alla Filosofia della Fisica. Roma: Carocci.Google Scholar

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© Springer Netherlands 2011

Authors and Affiliations

  1. 1.Department of Philosophy, Logic and Scientific MethodLondon School of EconomicsLondonUK

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