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PSA 1974 pp 15-32 | Cite as

Thermodynamics, Statistical Mechanics and the Complexity of Reductions

  • Lawrence Sklar
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 32)

Abstract

That reductions of theories and unifications of science frequently occur by means of identifications is a widely accepted hypothesis of methodology. Usually we are concerned with the micro-reductions of things, in which an entity is identified with a structured aggregate of smaller constituents. And, it is frequently alleged, we must also take into account further identifications in which the attributes of the macro-object, expressed by predicates in the macro-theory, are identified with attributes of the aggregate of micro-entities differently expressed by predicates of the micro- or reducing theory.

Keywords

Statistical Mechanic Thermodynamic Limit Thermodynamic Quantity Thermodynamic Entropy Macroscopic Theory 
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.

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Notes

  1. 3.
    A. Münster, Statistical Thermodynamics, Vol. I, English edition, Springer-Verlag, Heidelberg (1969), sec. 2.11.Google Scholar
  2. 4.
    A. Münster, op. cit., chap. IV. See also D. Ruelle, Statistical Mechanics, Rigorous Results, Benjamin, New York (1969), chap. 5.Google Scholar
  3. 5.
    A. Münster, op. cit., p. 213.Google Scholar
  4. 6.
    A. Münster, op. cit., secs. 2.1-3.2 and 4.1-4.4. See also D. Ruelle, op. cit., chaps. 1-3.Google Scholar
  5. 9.
    See H. Grad, ‘The Many Faces of Entropy’, Communications on Pure and Applied Mathematics 14 (1961), 323-354, esp. pp. 324-328. See also E. Jaynes, ‘Gibbs vs. Boltzmann Entropies’, American Journal of Physics, 33 (1965), 391-398, esp. sec. VI, pp. 397-398.Google Scholar
  6. 10.
    On the failure of the one-particle distribution function to give the correct entropy when inter-particle forces are taken into account see E. Jaynes, op. cit., pp. 391-394. See also his ‘Information Theory and Statistical Mechanics’, in K. Ford (ed.), Brandeis University Summer Institute Lectures in Theoretical Physics, 1962, vol. 3,’ statistical Physics’, pp. 181-218, esp. sec. 6, ‘Entropy and Probability’, pp. 212-217. For a discussion of how to move to the entropy defined by means of the two-particle distribution function and the generalization of this process see H. Grad, op. cit., passim.Google Scholar
  7. 11.
    On the definition of the Gibbs entropy and its relation to the Boltzmann see R. Tolman, op. cit., sec. 51, pp. 165-179, esp. (d) on pp. 174-177. There are in fact several different definitions for a Gibbs entropy, all of which “converge in the thermodynamic limit.” See J. Gibbs, op. cit., chap. XIV.Google Scholar
  8. 12.
    See E. Jaynes, ‘Gibbs vs. Boltzmann Entropies’, sec. V, pp. 395-397.Google Scholar
  9. 13.
    On the limits of extending thermodynamics entropy to non-equilibrium cases see P. Landsberg, Thermodynamics, Interscience, New York (1961), sec. 21, pp. 128-142. See also the work of Truesdell cited in note 19, below for important criticism of the “orthodox” view that thermodynamic quantities are “well defined” only in equilibrium situations.Google Scholar
  10. 14.
    For a defense of the thesis that by use of the fine-grained entropy one is perfectly able to establish the statistical mechanical “analogue” of the Second Law, see E. Jaynes, ‘Gibbs vs. Boltzmann Entropies’, sec. IV, ‘The Second Law’, pp. 394-395. See also his ‘Information Theory and Statistical Mechanics’, sec. 6, pp. 212-217.Google Scholar
  11. 16.
    An introduction to coarse-graining can be found in N. van Kampen, ‘Fundamental Problems in Statistical Mechanics of Irreversible Processes’, in E. Cohen (ed.), Fundamental Problems in Statistical Mechanics, Vol. I, North-Holland, Amsterdam (1961), pp. 173-202. See also O. Penrose, Foundations of Statistical Mechanics, Pergamon, Oxford (1970), Chap. I, ‘Basic Assumptions’, attempts a rationalization of coarse-graining. See esp. chap. I, sec. 3, ‘Observation’, where the “coarseness” of macro-observation is used to justify coarse-graining in statistical mechanics.Google Scholar
  12. 18.
    Field, Hartry, ‘Theory Change and the Indeterminacy of Reference’, Journal of Philosophy 70, No. 14, pp. 462-481, esp. p. 466.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1976

Authors and Affiliations

  • Lawrence Sklar
    • 1
  1. 1.University of MichiganUSA

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