Ergodic hypothesis in classical statistical mechanics

Revista Brasileira de Ensino de Fisica

Volumn 29, Issue 2, 2007, Pages 189-201

  de Oliveira, César R ^a   Werlang, Thiago ^a  

^a FEDERAL UNIVERSITY OF SÃO CARLOS   (Brazil)

Author keywords

Ergodic hypothesis; Microcanonical ensemble; Statistical mechanics

Indexed keywords

EID: 35248896353     PISSN: 01024744     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Nova Iorque, 1997).
2. R.W. Batterman, Philosophy of Science 65, 183 (1998).
3. J. Bricmont, Physicalia Magazine 17, 159 (1995).
4. Chaos 15, 015101-015121. (2005).
5. I.P. Cornfeld, S.V. Fomin and Y.G. Sinai, Ergodic Theory (Springer-Verlag, Berlin, 1982).
6. A.A. de Castro Jr., Curso de Teoria da Medida (Projeto Euclides, IMPA, Rio de Janeiro, 2004).
7. C.R. de Oliveira, Rev. Bras. Ens. Fís. 21, 22 (1999).
8. R.L. Dobrushin, Atti Convegni Lincei 131, 227 (1997).
9. V. Donnay and C. Liverani, Comm. Math. Phys. 135, 267 (1991).
10. J. Earman and- M. Rédei, Brit. J. Phil. Sci. 47, 63 (1996).
11. P. Ehrenfest and T. Ehrenfest, The Conceptual Foundations of the Statistical Approach in Mechanics (Dover, Nova Iorque, 1990).
12. I.E. Farquhar, Ergodic Theory in Statistical Mechanics (Interscience, Nova Iorque, 1964).
13. L. Galgani, A. Giorgili, A. Martinoli and S. Vanzini, Physics, D 59, 334 (1992).
14. G. Gallavotti, Statistical Mechanics. A Short Treatise (Springer-Verlag, Berlin, 1999); J. Statist. Phys. 78, 1571 (1995).
15. H.-O. Georgii,'Th. Rel. Fields 99, 171 (1994).
16. Y.M. Guttmann, The Concept of Probability in Statistical Physics (Cambridge University Press, Cambridge, 1999).
17. G. Keller, Equilibrium States in Ergodic Theory (Cambridge University Press, Cambridge, 1998).
18. A.I. Kinchin, Mathematical Foundations of Statistical Mechanics (Dover, Nova Iorque, 1949).
19. R. Kotecky, in Highlights of Mathematical Physics, edited by A. Fokas, J. Halliwell, T. Kibble and B. Zegarlinski. (Am. Math. Soc., Providence, 2002), p. 191-207.
20. N.S. Krylov, Works On the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979).
21. U. Krengel, Ergodic Theorems (de Gruyter, Berlin, 1985).
22. J.L. Lebowitz, Physics Today 46, 32 (1993).
23. J.L. Lebowitz and O. Penrose, Physics Today 26, 23 (1973).
24. O. Lombardi, Critica: Revista Hispanoamericana de Filosofia 35, 3 (2003).
25. D.B. Malament and S.L. Zabell, Philosophy of Science 47, 339 (1980).
26. R. Mañé, Matemática. Universitária 4, 64 (1986).
27. R. Mañé, Ergodic Theory and Differentiable Dynamics (Springer-Verlag, Berlin, 1987).
28. L. Markus and K.R. Meyer, Generic Hamiltonian Dynamical Systems Are Neither Integrable Nor Ergodic (AMS, Providence, 1974), Mem. Amer. Math. Soc., v. 144.
29. K. Oliveira, Um Primeiro Curso em Teoria Eryódica (IMPA, Rio de Janeiro, 2005).
30. J.C. Oxtoby and S.M. Ulam, Ann. Math. 42, 874 (1941).
31. J.J. Prentis, Am. J. Phys. 68, 1073 (2000).
32. W. Rudin, Real and Complex Analysis (McGraw-Hill, Nova Iorque, 1987).
33. D. Ruelle, Statistical Mechanics (Benjamin, Nova Iorque, 1969).
34. M.B. Sevryuk, Mosc. Math. J. 3, 1113 (2003).
35. N. Simányi, preprint mp-arc 05-430.
36. L. Sklar, Philosophy of Science 40, 194 (1973).
37. L. Sklar, Physics and Chance (Cambridge University Press, Cambridge, 1993).
38. D. Szász, Studia. Sci. Math. Hungar. 31, 299 (1996).
39. R.C. Tolman, The Principles of Statistical Mechanics (Dover, Nova Iorque, 1979).
40. J. Uffink, The Stanford Encyclopedia of Philosophy (Winter 2004 Edition), edited by Edward N. Zalta, http://plato.stanford.edu/archives/ win2004/entries/statphys-Boltzmann
41. J. von Plato, Arch. Hist. Ex. Sci. 44, 71 (1992).
42. P. Walters, An Introduction to Ergodic Theory (Springer-Verlag, Berlin, 1982).