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Volumn 40, Issue 2, 2009, Pages 174-191

Boltzmann's H-theorem, its discontents, and the birth of statistical mechanics

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EID: 67349276423     PISSN: 13552198     EISSN: 18792502     Source Type: Journal    
DOI: 10.1016/j.shpsb.2009.03.003     Document Type: Article
Times cited : (76)

References (73)
  • 1
    • 0003391464 scopus 로고    scopus 로고
    • Harvard University Press, Cambridge, Mass
    • Albert D.Z. Time and chance (2000), Harvard University Press, Cambridge, Mass
    • (2000) Time and chance
    • Albert, D.Z.1
  • 5
    • 84857636926 scopus 로고    scopus 로고
    • Boltzmann, L. (1868). Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten. Sitzungberichte der Akademie der Wissenschaften zu Wien. mathematisch-naturwissenschaftliche Klasse, 58, 517-560 (Reprinted in Boltzmann (1909), 1, pp. 49-96).
    • Boltzmann, L. (1868). Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten. Sitzungberichte der Akademie der Wissenschaften zu Wien. mathematisch-naturwissenschaftliche Klasse, 58, 517-560 (Reprinted in Boltzmann (1909), Vol. 1, pp. 49-96).
  • 6
    • 0011854946 scopus 로고
    • Analytischer Beweis der zweiten Hauptsatzes der mechanischen Wärmetheorie aus den Sätzen über das Gleichgewicht der lebendigen Kraft
    • Reprinted in Boltzmann 1909, 1, pp. 288-308
    • Boltzmann, L. (1871). Analytischer Beweis der zweiten Hauptsatzes der mechanischen Wärmetheorie aus den Sätzen über das Gleichgewicht der lebendigen Kraft. Sitzungberichte der Akademie der Wissenschaften zuWien, mathematisch-naturwissenschaftliche Klasse, 63, 712-732 (Reprinted in Boltzmann (1909), Vol. 1, pp. 288-308).
    • (1871) Sitzungberichte der Akademie der Wissenschaften zuWien, mathematisch-naturwissenschaftliche Klasse , vol.63 , pp. 712-732
    • Boltzmann, L.1
  • 7
    • 0000229982 scopus 로고
    • Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen
    • Reprinted in Boltzmann (1909, 1, pp. 316-402. English translation in Brush 2003, pp. 262-349
    • Boltzmann, L. (1872). Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. Sitzungberichte der Akademie der Wissenschaften zu Wien, mathematischnaturwissenschaftliche Klasse, 66, 275-370 (Reprinted in Boltzmann (1909), Vol. 1, pp. 316-402. English translation in Brush (2003), pp. 262-349).
    • (1872) Sitzungberichte der Akademie der Wissenschaften zu Wien, mathematischnaturwissenschaftliche Klasse , vol.66 , pp. 275-370
    • Boltzmann, L.1
  • 8
    • 0012254981 scopus 로고
    • Bemerkungen über einige Probleme der mechanische Wärmetheorie
    • Reprinted in Boltzmann (1909, 2, pp. 116-122. Partial English translation in Brush (2003, pp. 362-376 (NB: the title ascribed to this paper in Brush, 2003, pp. vi, 362 & 362n, is that of Boltzmann 1877b
    • Boltzmann, L. (1877a). Bemerkungen über einige Probleme der mechanische Wärmetheorie. Sitzungberichte der Akademie der Wissenschaften zu Wien, mathematisch-naturwissenschaftliche Klasse, 75, 62-100 (Reprinted in Boltzmann (1909), Vol. 2, pp. 116-122. Partial English translation in Brush (2003), pp. 362-376 (NB: the title ascribed to this paper in Brush, 2003, pp. vi, 362 & 362n, is that of Boltzmann (1877b))).
    • (1877) Sitzungberichte der Akademie der Wissenschaften zu Wien, mathematisch-naturwissenschaftliche Klasse , vol.75 , pp. 62-100
    • Boltzmann, L.1
  • 9
    • 84857635609 scopus 로고    scopus 로고
    • Boltzmann, L. (1877b). Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Satze der Wärmetheorie. Sitzungberichte der Akademie der Wissenschaften zu Wien. mathematisch-naturwissenschaftliche Klasse, 76, 373-435 (Reprinted in Boltzmann (1909), 2, pp. 164-223).
    • Boltzmann, L. (1877b). Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Satze der Wärmetheorie. Sitzungberichte der Akademie der Wissenschaften zu Wien. mathematisch-naturwissenschaftliche Klasse, 76, 373-435 (Reprinted in Boltzmann (1909), Vol. 2, pp. 164-223).
  • 10
    • 0000538148 scopus 로고
    • On certain questions of the theory of gases
    • Boltzmann L. On certain questions of the theory of gases. Nature 51 1322 (1895) 413-415
    • (1895) Nature , vol.51 , Issue.1322 , pp. 413-415
    • Boltzmann, L.1
  • 11
    • 34547372017 scopus 로고
    • On the minimum theorem in the theory of gases
    • Boltzmann L. On the minimum theorem in the theory of gases. Nature 52 1340 (1895) 221
    • (1895) Nature , vol.52 , Issue.1340 , pp. 221
    • Boltzmann, L.1
  • 12
    • 84857633540 scopus 로고    scopus 로고
    • Boltzmann, L. (1896). Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn. E. Zermelo. Wiedemann's Annalen, 57, 773-784; (also in Boltzmann (1909), III, paper 119).
    • Boltzmann, L. (1896). Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn. E. Zermelo. Wiedemann's Annalen, 57, 773-784; (also in Boltzmann (1909), Vol. III, paper 119).
  • 13
    • 84979125933 scopus 로고
    • Zu Hrn Zermelos Abhandlung Über die mechanische Erklärung irreversibler Vorgänge
    • (Reprinted in Boltzmann (1909), Vol. III pp. 579-584. English translation in Brush (2003), pp. 412-419).
    • Boltzmann L. Zu Hrn Zermelos Abhandlung Über die mechanische Erklärung irreversibler Vorgänge. Annalen der Physik 60 (1897) 392-398 (Reprinted in Boltzmann (1909), Vol. III pp. 579-584. English translation in Brush (2003), pp. 412-419).
    • (1897) Annalen der Physik , vol.60 , pp. 392-398
    • Boltzmann, L.1
  • 14
    • 84857628370 scopus 로고    scopus 로고
    • Boltzmann L. (1909). In: F. Hasenöhrl (Ed.), Wissenschaftliche Abhandlungen I, II, and III. Leipzig: Barth (Reissued New York: Chelsea; 1969).
    • Boltzmann L. (1909). In: F. Hasenöhrl (Ed.), Wissenschaftliche Abhandlungen Vol. I, II, and III. Leipzig: Barth (Reissued New York: Chelsea; 1969).
  • 15
    • 0011105078 scopus 로고
    • Science of chaos or chaos in science?
    • (Reprinted in P.R. Gross, N. Levitt, & M. W. Lewis (Eds.). The flight from science and reason (pp. 131-176). New York: New York Academy of Sciences; New York).
    • Bricmont J. Science of chaos or chaos in science?. Physicalia 17 (1995) 159-208 (Reprinted in P.R. Gross, N. Levitt, & M. W. Lewis (Eds.). The flight from science and reason (pp. 131-176). New York: New York Academy of Sciences; New York).
    • (1995) Physicalia , vol.17 , pp. 159-208
    • Bricmont, J.1
  • 16
    • 0002931947 scopus 로고
    • and 2, Oxford: Pergamon
    • Brush, S.G. (1966). Kinetic theory (Vol. 1 and 2). Oxford: Pergamon.
    • (1966) Kinetic theory , vol.1
    • Brush, S.G.1
  • 18
    • 51149127955 scopus 로고
    • The kinetic theory of gases
    • Bryan G.H. The kinetic theory of gases. Nature 51 1312 (1894) 176
    • (1894) Nature , vol.51 , Issue.1312 , pp. 176
    • Bryan, G.H.1
  • 19
    • 84857634058 scopus 로고
    • Samuel Hawksley Burbury 1831-1911
    • (The obituary notice was attributed to "G. H. B.".)
    • Bryan G.H. Samuel Hawksley Burbury 1831-1911. Proceedings of the Royal Society of London Series A 88 606 (1913) i-iv (The obituary notice was attributed to "G. H. B.".)
    • (1913) Proceedings of the Royal Society of London Series A , vol.88 , Issue.606
    • Bryan, G.H.1
  • 20
    • 0001990032 scopus 로고
    • Boltzmann's minimum function
    • Burbury S.H. Boltzmann's minimum function. Nature 51 1308 (1894) 78
    • (1894) Nature , vol.51 , Issue.1308 , pp. 78
    • Burbury, S.H.1
  • 21
    • 33646163995 scopus 로고
    • Boltzmann's minimum function
    • Burbury S.H. Boltzmann's minimum function. Nature 51 1318 (1895) 320
    • (1895) Nature , vol.51 , Issue.1318 , pp. 320
    • Burbury, S.H.1
  • 22
    • 51149162385 scopus 로고
    • Boltzmann's minimum function
    • Burbury S.H. Boltzmann's minimum function. Nature 52 1335 (1895) 104-105
    • (1895) Nature , vol.52 , Issue.1335 , pp. 104-105
    • Burbury, S.H.1
  • 24
    • 0042574883 scopus 로고    scopus 로고
    • Reducing thermodynamics to statistical mechanics: the case of entropy
    • Callender C. Reducing thermodynamics to statistical mechanics: the case of entropy. Journal of Philosophy 96 (1999) 348-373
    • (1999) Journal of Philosophy , vol.96 , pp. 348-373
    • Callender, C.1
  • 25
    • 51149156298 scopus 로고
    • Dr. Watson's proof of Boltzmann's theorem on the permanence of distributions
    • Culverwell E.P. Dr. Watson's proof of Boltzmann's theorem on the permanence of distributions. Nature 50 1304 (1894) 617
    • (1894) Nature , vol.50 , Issue.1304 , pp. 617
    • Culverwell, E.P.1
  • 26
    • 51149132264 scopus 로고
    • Boltzmann's minimum theorem
    • Culverwell E.P. Boltzmann's minimum theorem. Nature 51 1315 (1894) 246
    • (1894) Nature , vol.51 , Issue.1315 , pp. 246
    • Culverwell, E.P.1
  • 28
    • 0348016943 scopus 로고
    • Will someone say exactly what the H-theorem proves? A study of Burbury's Condition A and Maxwell's Proposition II
    • 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. Archive for History of Exact Sciences 46 (1994) 341-366
    • (1994) Archive for History of Exact Sciences , vol.46 , pp. 341-366
    • Dias, P.M.C.1
  • 30
    • 67349229704 scopus 로고
    • A comment on Boltzmann's H-theorem and time reversal
    • Eggarter T.P. A comment on Boltzmann's H-theorem and time reversal. American Journal of Physics 41 (1973) 874-877
    • (1973) American Journal of Physics , vol.41 , pp. 874-877
    • Eggarter, T.P.1
  • 31
    • 84857633726 scopus 로고    scopus 로고
    • Ehrenfest, P. & Ehrenfest, T. (1990). The Conceptual Foundations of the Statistical Approach in Mechanics. Toronto: Dover Publications, Inc. This is a republication of the English translation published by Cornell University Press (Ithaca, NY) in 1959. The original German publication was. In: F. Klein, & C. Müller (Eds.) (1912) Begriffliche Grundlagen der Statistischen Auffassung in der Mechanik, Enzyclopädie der Mathematischen Wissensschaften (4, pp. 3-90). Leibzig: Teubner, pp. 3-90.
    • Ehrenfest, P. & Ehrenfest, T. (1990). The Conceptual Foundations of the Statistical Approach in Mechanics. Toronto: Dover Publications, Inc. This is a republication of the English translation published by Cornell University Press (Ithaca, NY) in 1959. The original German publication was. In: F. Klein, & C. Müller (Eds.) (1912) Begriffliche Grundlagen der Statistischen Auffassung in der Mechanik, Enzyclopädie der Mathematischen Wissensschaften (Vol. 4, pp. 3-90). Leibzig: Teubner, pp. 3-90.
  • 33
    • 84857627676 scopus 로고    scopus 로고
    • Probability in Boltzmannian statistical mechanics
    • G. Ernst & A. Hüttemann Eds, Cambridge: Cambridge University Press, forthcoming
    • Frigg, R. P. (2009). Probability in Boltzmannian statistical mechanics, In G. Ernst & A. Hüttemann (Eds.), Time, chance and reduction. Philosophical aspects of statistical mechanics. Cambridge: Cambridge University Press, forthcoming.
    • (2009) Time, chance and reduction. Philosophical aspects of statistical mechanics
    • Frigg, R.P.1
  • 35
    • 67349087853 scopus 로고    scopus 로고
    • Dog, fleas and tree trunks: The Ehrenfests marking the territory of Boltzmann's H-theorem
    • Unpublished
    • Janssen, M. (2002). Dog, fleas and tree trunks: The Ehrenfests marking the territory of Boltzmann's H-theorem. Unpublished.
    • (2002)
    • Janssen, M.1
  • 38
    • 84989462410 scopus 로고
    • Mechanical explanation at the end of the nineteenth century
    • Klein M.J. Mechanical explanation at the end of the nineteenth century. Centaurus 17 (1973) 58-82
    • (1973) Centaurus , vol.17 , pp. 58-82
    • Klein, M.J.1
  • 39
    • 0346755999 scopus 로고
    • The development of Boltzmann's statistical ideas
    • Cohen E.G.D., and Thirring W. (Eds), Springer, Wien
    • Klein M.J. The development of Boltzmann's statistical ideas. In: Cohen E.G.D., and Thirring W. (Eds). The Boltzmann equation (1973), Springer, Wien 53-106
    • (1973) The Boltzmann equation , pp. 53-106
    • Klein, M.J.1
  • 45
    • 0000978423 scopus 로고
    • Tait's "Thermodynamics" II
    • Maxwell J.C. Tait's "Thermodynamics" II. Nature XVII 431 (1878) 278-280
    • (1878) Nature , vol.XVII , Issue.431 , pp. 278-280
    • Maxwell, J.C.1
  • 48
    • 84857636308 scopus 로고    scopus 로고
    • Poincaré, H. (1889). Sur les tentatives d'explication mécanique des principes de la thermodynamique, Comptes rendus de l'Académie des sciences (Paris) 108, 550-553. An English translation is found in the Appendix in Olsen, 1993.
    • Poincaré, H. (1889). Sur les tentatives d'explication mécanique des principes de la thermodynamique, Comptes rendus de l'Académie des sciences (Paris) 108, 550-553. An English translation is found in the Appendix in Olsen, 1993.
  • 49
    • 77951516344 scopus 로고
    • Sur le problème des trois corps et les équations de la dynamique
    • English translation of extracts relevant to Zermelo's recurrence argument in Olsen, 1993, pp. 368-376.
    • Poincaré H. Sur le problème des trois corps et les équations de la dynamique. Acta Mathematica 13 (1890) 1-270 English translation of extracts relevant to Zermelo's recurrence argument in Olsen, 1993, pp. 368-376.
    • (1890) Acta Mathematica , vol.13 , pp. 1-270
    • Poincaré, H.1
  • 50
    • 84857627623 scopus 로고
    • Thermodynamique. Leçons professées pendant le premier semestre 1888-89 par H
    • Compiled by J. Blondin. Paris: G. Carré
    • Poincaré, H. (1892a). Thermodynamique. Leçons professées pendant le premier semestre 1888-89 par H. Poincaré. Compiled by J. Blondin. Paris: G. Carré.
    • (1892) Poincaré
    • Poincaré, H.1
  • 51
    • 51149152816 scopus 로고
    • Poincaré's "Thermodynamics"
    • Poincaré H. Poincaré's "Thermodynamics". Nature 45 1169 (1892) 485
    • (1892) Nature , vol.45 , Issue.1169 , pp. 485
    • Poincaré, H.1
  • 52
    • 0010721112 scopus 로고
    • Le mécanisme et l'expérience
    • English translation in Brush (1966), pp. 203-207.
    • Poincaré H. Le mécanisme et l'expérience. Revue de Métaphysique et de Morale 1 (1893) 534-537 English translation in Brush (1966), pp. 203-207.
    • (1893) Revue de Métaphysique et de Morale , vol.1 , pp. 534-537
    • Poincaré, H.1
  • 53
    • 1542565277 scopus 로고
    • On the stability of the solar system
    • (Translation of paper in Annuaire du Bureau des Longitudes, 1898; this original paper was reprinted in Poincaré, H. (2002). Scientific opportunism/L'Opportunisme scientifique, An Anthology. Series: Publications des Archives Henri Poincaré/Publications of the Henri Poincaré Archives. Birkhäuser, Chapter V).
    • Poincaré H. On the stability of the solar system. Nature 58 1495 (1898) 183-185 (Translation of paper in Annuaire du Bureau des Longitudes, 1898; this original paper was reprinted in Poincaré, H. (2002). Scientific opportunism/L'Opportunisme scientifique, An Anthology. Series: Publications des Archives Henri Poincaré/Publications of the Henri Poincaré Archives. Birkhäuser, Chapter V).
    • (1898) Nature , vol.58 , Issue.1495 , pp. 183-185
    • Poincaré, H.1
  • 56
    • 4043067401 scopus 로고    scopus 로고
    • Burbury's last case: the mystery of the entropic arrow
    • Craig C. (Ed), Cambridge University Press, Cambridge
    • Price H. Burbury's last case: the mystery of the entropic arrow. In: Craig C. (Ed). Time, reality and experience (2002), Cambridge University Press, Cambridge 19-56
    • (2002) Time, reality and experience , pp. 19-56
    • Price, H.1
  • 57
    • 39549089587 scopus 로고    scopus 로고
    • The thermodynamic arrow: puzzles and pseudo-puzzles
    • Bigi I., and Faessler M. (Eds), World Scientific, Singapore
    • Price H. The thermodynamic arrow: puzzles and pseudo-puzzles. In: Bigi I., and Faessler M. (Eds). Time and matter (2006), World Scientific, Singapore 209-224
    • (2006) Time and matter , pp. 209-224
    • Price, H.1
  • 58
    • 0039116087 scopus 로고
    • The Ehrenfests' wind-tree model and the hypothesis of molecular chaos
    • Rechtman R., Salcido A., and Calles A. The Ehrenfests' wind-tree model and the hypothesis of molecular chaos. European Journal of Physics 12 1991 (1991)
    • (1991) European Journal of Physics , vol.12 , Issue.1991
    • Rechtman, R.1    Salcido, A.2    Calles, A.3
  • 59
    • 45749098378 scopus 로고    scopus 로고
    • Ludwig Boltzmann: a life of passion
    • Reiter W.L. Ludwig Boltzmann: a life of passion. Physics in Perspective 9 (2007) 357-374
    • (2007) Physics in Perspective , vol.9 , pp. 357-374
    • Reiter, W.L.1
  • 62
    • 84880378866 scopus 로고
    • Poincaré's "Thermodynamics"
    • Tait P.G. Poincaré's "Thermodynamics". Nature 45 1167 (1892)
    • (1892) Nature , vol.45 , Issue.1167
    • Tait, P.G.1
  • 63
    • 36149015658 scopus 로고
    • Foundations of statistical mechanics
    • ter Haar D. Foundations of statistical mechanics. Reviews of Modern Physics 27 (1955) 289-338
    • (1955) Reviews of Modern Physics , vol.27 , pp. 289-338
    • ter Haar, D.1
  • 65
    • 36149045236 scopus 로고
    • A generalization of the Ehrenfests' wind-tree model
    • van Holten J.W., and van Saarloos W. A generalization of the Ehrenfests' wind-tree model. European Journal of Physics 1 3 (1980) 149-152
    • (1980) European Journal of Physics , vol.1 , Issue.3 , pp. 149-152
    • van Holten, J.W.1    van Saarloos, W.2
  • 68
    • 66749093621 scopus 로고    scopus 로고
    • Compendium of the foundations of statistical physics
    • Butterfield J., and Earman J. (Eds), North-Holland, Amsterdam
    • Uffink J. Compendium of the foundations of statistical physics. In: Butterfield J., and Earman J. (Eds). Handbook of the philosophy of science (2007), North-Holland, Amsterdam 924-1074
    • (2007) Handbook of the philosophy of science , pp. 924-1074
    • Uffink, J.1
  • 70
    • 51149147733 scopus 로고
    • Boltzmann's minimum theorem
    • Watson H.W. Boltzmann's minimum theorem. Nature 51 1309 (1894) 105
    • (1894) Nature , vol.51 , Issue.1309 , pp. 105
    • Watson, H.W.1
  • 72
    • 84965012545 scopus 로고
    • Über einen Satz der Dynamik und die mechanische Wärmetheorie
    • (English translation in Brush, S. G. (2003). The kinetic theory of gases (pp. 382-391). London: Imperial College Press.
    • Zermelo E. Über einen Satz der Dynamik und die mechanische Wärmetheorie. Annalen der Physik 57 (1896) 485-494 (English translation in Brush, S. G. (2003). The kinetic theory of gases (pp. 382-391). London: Imperial College Press.
    • (1896) Annalen der Physik , vol.57 , pp. 485-494
    • Zermelo, E.1
  • 73
    • 11844279398 scopus 로고
    • Uber mechanische Erklärungen irreversibler Vorgänge
    • (English translation in Brush, S. G. (2003). The kinetic theory of gases (pp. 403-411). London: Imperial College Press.)
    • Zermelo E. Uber mechanische Erklärungen irreversibler Vorgänge. Annalen der Physik 59 (1896) 4793-4801 (English translation in Brush, S. G. (2003). The kinetic theory of gases (pp. 403-411). London: Imperial College Press.)
    • (1896) Annalen der Physik , vol.59 , pp. 4793-4801
    • Zermelo, E.1


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