Probabilistic issues in statistical mechanics

Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

Volumn 36, Issue 2, 2005, Pages 303-322

  Emch, Gérard G ^a  

^a ALL SOULS COLLEGE   (United Kingdom)

Author keywords

Semantic of probability; Statistical mechanics

Indexed keywords

EID: 19144371514     PISSN: 13552198     EISSN: 18792502     Source Type: Journal    
DOI: 10.1016/j.shpsb.2004.06.003     Document Type: Article

References (72)

1. V.I. Arnold & A. Avez Ergodic problems of classical mechanics 1968 Benjamin New York
2. Bayes, T. (1763, 1765). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370-418; 54, 296-335.
3. D. Bernoulli Hydrodynamica 1768 Dulceker Argentoratum
4. J. Bernoulli Ars conjectandi 1713 Imp. Thurnis Fraet Basileae
5. L. Boltzmann Studien über das Gleichgewicht der lebendigen Kraft zwischen bewegten materiellen Punkten Sitzungberichte der Akademie der Wissenschaften in Wien 58 1868 517-560
6. L. Boltzmann Einige allgemeine Sätze über Wärmegleichgewicht unter Gasmolekulen Sitzungberichte Akademie der Wissenschaften in Wien, Mathematisch-Naturwissenschaftliche Klasse 63 1871 679-711
7. L. Boltzmann Referat über die Abhandlung von J.C. Maxwell Wiedemannsche Annalen der Physik Beiblätter 5 1881 403-417
8. E. Borel Les probabilités dénombrables et leurs applications arithmétiques Rendiconti del Circolo Matematico di Palermo 27 1909 247-271
9. Brouwer, L. E. J. (1910, 1912). Beweis der Invarianz der Dimensionzahl. Mathematische Annalen 70, 161-170; 71, 305-313; 314-319; 72, 55-56.
10. H.R. Brown & J. Uffink The origins of time-asymmetry in thermodynamics: The minus first law Studies in History and Philosophy of Modern Physics 32B 2001 525-538
11. S.G. Brush Statistical physics and the atomic theory of matter, from Boyle and Newton to Landau and Onsager 1983 Princeton University Press Princeton
12. C. Calude Information and randomness: An algorithmic perspective 1994 Springer Berlin
13. Cardano, H. (1539, 1564). Practica arithmetice, & mensurandi singularis, Liber de ludo alae. Mediolani: Bernardini Calusci. Book on games of chance (S. H. Gould, Trans.). In O. Ore (Ed.) (1996), Cardano, the gambling scholar. Princeton: Princeton University Press.
14. G.J. Chaitin Information-theoretic computational complexity IEEE Transactions on Information Theory IT 20 1974 10-15
15. G.J. Chaitin Information, randomness and incompleteness 2nd ed. 1990 World Scientific Singapore
16. D.G. Champernowne The construction of decimals normal in the scale of ten Journal of the London Mathematical Society 8 1933 254-260
17. A. Church On the concept of random sequence Bulletin of the American Mathematical Society 47 1940 130-135
18. A.H. Copeland & P. Erdös Note on normal numbers Bulletin of the American Mathematical Society 92 1946 857-860
19. B. de Finetti La prévision, ses lois logiques et ses sources subjectives Annales de l'Institut Henri Poincaré 7 1937 1-68
20. de Finetti, B. (1972). Probability, induction, and statistics. New York: Wiley.
21. A. de Moivre The doctrine of chance; or, a method of calculating the probabilities of events of plays 2nd ed. 1738 Woodfall London
22. P. Diaconis & D. Freedman Finite exchangeable sequences Annals of Probability 8 1980 745-764
23. R. Dugas La théorie physique au sens de Boltzmann 1959 Griffon Neuchâtel
24. P. Ehrenfest & T. Ehrenfest Ueber zwei bekannte Einwände gegen das Boltzmannsche H-Theorem Physikalische Zeitschrift 8 1907 311-314
25. P. Ehrenfest & T. Ehrenfest Begriffliche Grundlagen der statistischen Auffassungen in der Mechanik 1911 Teubner Leipzig
26. G.G. Emch Algebraic methods in statistical mechanics and quantum field theory 1972 Wiley New York
27. G.G. Emch On the need to adapt de Finetti's probability interpretation to QM In R. Alicki et al. (Eds.) Quantum probability 1998 Banach Center, Polish Academy of Sciences Warsawa 157-168
28. Emch, G. G. (2003). Is there a quantum de Finetti programme? Foundations of probability and physics, mathematical modeling in physics, engineering, and cognitive sciences. (Vol. 5, pp. 159-178). Växjö: University Press.
29. G. Emch & C. Liu The logic of thermostatistical physics 2002 Springer Berlin
30. Feller, W. (1968, 1971). An introduction to probability theory and its applications. (2 Vols). New York: Wiley.
31. Gauss, C. F. (1809). Theoria motus corporum coelestrium. Hamburg: F. Perthes and I. H. Besser.
32. J.W. Gibbs Elementary principles of statistical mechanics, developed with special reference to the rational foundations of thermodynamics 1902 Scribner New York
33. P. Hertz Ueber die mechanische grundlagen der thermodynamik Annalen der Physik 33 1910 537-552
34. R.E. Hodel An introduction to mathematical logic 1995 PWS Publishers Boston
35. R.L. Hudson Analogs of the de Finetti theorem and the interpretative problems of quantum mechanics Foundations of Physics 11 1981 805-808
36. R.L. Hudson & G.R. Moody Locally normal symmetric states and an analog of de Finetti's theorem Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 33 1976 343-351
37. C. Huygens Tractatus de ratiocinus in alae ludo 1657 Elsevier Amsterdam
38. E.T. Jaynes Papers on probability, statistics and statistical physics 1989 Kluwer Dordrecht
39. R.V. Kadison & J.R. Ringrose Fundamentals of the theory of operator algebras: I. Elementary theory; II. Advanced theory 1983, 1986 Wiley New York
40. Khinchin, A. (1957). Mathematical foundations of information theory (R. A. Silverman & M. D. Friedman, Trans.). New York: Dover.
41. King, C., & Ruskai, M. B. (Guest Eds.) (2002). Quantum information theory. [Special issue]. Journal of Mathematical Physics 43, 4237-4566.
42. A.N. Kolmogorov Gründbegriffe der Wahrscheinlichkeitsrechnung 1933 Springer Berlin
43. P.S. Laplace Théorie analytique des probabilités 3me ed. 1820 Courcier Paris
44. G.W. Leibniz Dissertatio de arte combinatoria 1666 Frick & Seubold Lipsia
45. M. Li & P. Vitanyi An introduction to Kolmogorov complexity and its applications 2nd ed. 1997 Springer New York
46. E.H. Lieb & J. Yngvason The physics and mathematics of the second law of thermodynamics Physics Reports 310 1999 1-96
47. E.H. Lieb & J. Yngvason A fresh look at entropy and the second law of thermodynamics Physics Today 53 2000 32-37
48. Markus, L., & Meyer, K. R. (1974). Generic Hamiltonian systems are neither integrable nor ergodic. Memoirs of the American mathematical society (Vol. 144). Providence: AMS.
49. P. Martin-Löf The definition of random sequences Information and Control 9 1966 602-619
50. P. Martin-Löf Complexity oscillations in infinite binary sequences Zeitschrift für Wahrscheinlichkeits - theorie und verwandte Gebiete 19 1971 225-230
51. Maxwell, J. C. (1860). Illustrations of the dynamical theory of gases, I, II. Philosophical magazine 19, 19-32, 20, 21-37.
52. J.C. Maxwell On Boltzmann's theorem on the average distribution of energy in a system of material points Transactions of the Cambridge Philosophical Society 12 1879 547-570
53. M. Ohya & D. Petz Quantum entropy and its uses 1993 Springer Berlin
54. B. Pascal Traité du triangle arithmétique 1665 Desprez Paris
55. G.F. Peverone Due brevi e facili trattati: Il primo d'arithmetica, l'altro di geometria 1558 de Tournes Lione
56. M. Plancherel Beweis der Unmöglichkeit ergodischer mechanischer Systeme Annalen der Physik 42 1913 1061-1063
57. Schrödinger, E. (1935). Die Gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807-812; 823-828; 844-849 (J. D. Trimmer, Trans.). The present situation in quantum mechanics: A translation of Schrödinger "cat paradox" paper. Proceedings of the American Philosophical Society 124, 323-338.
58. C.E. Shannon & W. Weaver The mathematical theory of communication 1949 University of Illinois Press Urbana
59. E. Størmer Symmetric states on infinite tensor products of C&-algebras Journal of Functional Analysis 3 1969 48-68
60. J. Uffink Can the maximum entropy principle be explained as a consistency requirement? Studies in History and Philosophy of Modern Physics 26B 1995 223-261
61. J. Uffink The constraint rule of the maximum entropy principle Studies in History and Philosophy of Modern Physics 27 1996 47-79
62. M. van Lambalgen The axiomatization of randomness Journal of Symbolic Logic 55 1990 1143-1167
63. van Lambalgen, M. (1996) Randomness and foundations of probability: Von Mises' axiomatisation of random sequences. In T. Ferguson, et al. (Eds.). Probability, statistics and game theory: Papers in honour of David Blackwell, Monograph Series (Vol. 30, pp. 347-367). Hayward, CA: Institute for Mathematical Statistics.
64. V.S. Varadarajan Geometry of quantum theory 2nd ed. 1985 Springer New York
65. J. Ville Etude critique de la notion de collectif 1939 Gauthier-Villars Paris
66. R. von Mises Wahrscheinlichkeit, Statistik und ihre Wahrheit 1928 J. Springer Wien
67. R. von Mises Kleines Lehrbuch der Positivismus, Einführung in die empirische Wissenschaftausfassung 1939 University of Chicago Press Chicago
68. J. von Neumann Mathematische Grundlagen der Quantenmechanik 1932 Springer Berlin
69. von Neumann, J. (1937). Quantum logic (strict- and probabilistic logic). Unpublished manuscript deposited in the John von Neumann Archives, Library of Congress, Washington, DC, dated ca. 1937, and reviewed by A. H. Taub (1961) in J. von Neumann: Collected works (Vol. IV). Cambridge: Pergamon.
70. J. von Neumann Various techniques used in connection with random digits Journal of Research of the National Bureau of Standards Applied Mathematical Series 3 1951 36-38
71. J. von Plato Creating modern probability its mathematics, physics, and philosophy in historical perspective 1994 Cambridge University Press Cambridge
72. A. Wald Die Widerspruchsfreiheit des Kollektivbegriffes Actualités Scientifiques et Industrielles 735 1938 79-99