Microscopic origins of irreversible macroscopic behavior

Physica A: Statistical Mechanics and its Applications

Volumn 263, Issue 1-4, 1999, Pages 516-527

  Lebowitz, Joel L ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002542839     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(98)00514-7     Document Type: Article

References (48)

1. W. Thomson, Proc. of the Royal Soc. of Edinburgh, 8, 325 (1874).
2. S.G. Brush, Kinetic Theory, Pergamon, Oxford, (1966).
3. For an interesting biography of Boltzmann, which also contains many references, see E. Broda Ludwig Boltzmann, Man - Physicist - Philosopher, Ox Bow Press, Woodbridge, Conn (1983); translated from the German.
4. For a historical discussion of Boltzmann and his ideas see articles by M. Klein, E. Broda, L. Flamn in The Boltzmann Equation, Theory and Application, E.G.D. Cohen and W. Thirring, eds., Springer-Verlag, 1973.
5. For a general history of the subject see S.G. Brush, The Kind of Motion We Call Heat, Studies in Statistical Mechanics, vol. VI, E.W. Montroll and J.L. Lebowitz, eds. North-Holland, Amsterdam, (1976).
6. For some of my own articles on this subject see J. L. Lebowitz, Physica A 194, 1-97 (1993); Boltzmann's Entropy and Time's Arrow, Physics Today, 46, 32-38 (1993); Lebowitz's replies to readers' responses to the previous article, Physics Today, 47:113-116, 1994; Microscopic Reversibility and Macroscopic Behavior: Physical Explanations and Mathematical Derivations, in 25 Years of Non-Equilibrium Statistical Mechanics, Proceedings, Sitges Conference, Barcelona, Spain, 1994, in Lecture Notes in Physics, J.J. Brey, J. Marro, J.M. Rubí and M. San Miguel eds., Springer, (1995).
7. For some of my own articles on this subject see J. L. Lebowitz, Physica A 194, 1-97 (1993); Boltzmann's Entropy and Time's Arrow, Physics Today, 46, 32-38 (1993); Lebowitz's replies to readers' responses to the previous article, Physics Today, 47:113-116, 1994; Microscopic Reversibility and Macroscopic Behavior: Physical Explanations and Mathematical Derivations, in 25 Years of Non-Equilibrium Statistical Mechanics, Proceedings, Sitges Conference, Barcelona, Spain, 1994, in Lecture Notes in Physics, J.J. Brey, J. Marro, J.M. Rubí and M. San Miguel eds., Springer, (1995).
8. For some of my own articles on this subject see J. L. Lebowitz, Physica A 194, 1-97 (1993); Boltzmann's Entropy and Time's Arrow, Physics Today, 46, 32-38 (1993); Lebowitz's replies to readers' responses to the previous article, Physics Today, 47:113-116, 1994; Microscopic Reversibility and Macroscopic Behavior: Physical Explanations and Mathematical Derivations, in 25 Years of Non-Equilibrium Statistical Mechanics, Proceedings, Sitges Conference, Barcelona, Spain, 1994, in Lecture Notes in Physics, J.J. Brey, J. Marro, J.M. Rubí and M. San Miguel eds., Springer, (1995).
9. For some of my own articles on this subject see J. L. Lebowitz, Physica A 194, 1-97 (1993); Boltzmann's Entropy and Time's Arrow, Physics Today, 46, 32-38 (1993); Lebowitz's replies to readers' responses to the previous article, Physics Today, 47:113-116, 1994; Microscopic Reversibility and Macroscopic Behavior: Physical Explanations and Mathematical Derivations, in 25 Years of Non-Equilibrium Statistical Mechanics, Proceedings, Sitges Conference, Barcelona, Spain, 1994, in Lecture Notes in Physics, J.J. Brey, J. Marro, J.M. Rubí and M. San Miguel eds., Springer, (1995).
10. For a clear defense of Boltzmann's views against some recent attacks see the article by J. Bricmont, Science of Chaos or Chaos in Science? in The Flight from Science and Reason, Ann. N.Y. Academy of Sciences 79, p. 131 (1996). This article first appeared in the publication of the Belgian Physical Society, Physicalia Magazine, 17, 159, (1995), where it is followed by an exchange between Prigogine and Bricmont.
11. For a clear defense of Boltzmann's views against some recent attacks see the article by J. Bricmont, Science of Chaos or Chaos in Science? in The Flight from Science and Reason, Ann. N.Y. Academy of Sciences 79, p. 131 (1996). This article first appeared in the publication of the Belgian Physical Society, Physicalia Magazine, 17, 159, (1995), where it is followed by an exchange between Prigogine and Bricmont.
12. O. Penrose, Foundations of Statistical Mechanics, Pergamon, Elmsford, N.Y. (1970), ch. 5.
13. D. Levesque and L. Verlet, J. Stat. Phys. 72, 519 (1993); see also B.T. Nadiga, J.E. Broadwell and B. Sturtevant, Rarefield Gas Dynamics: Theoretical and Computational Techniques, edited by E.P. Muntz, D.P. Weaver and D.H. Campbell, Vol 118 of Progress in Astronautics and Aeronautics, AIAA, Washington, DC, ISBN 0-930403-55-X, 1989.
14. D. Levesque and L. Verlet, J. Stat. Phys. 72, 519 (1993); see also B.T. Nadiga, J.E. Broadwell and B. Sturtevant, Rarefield Gas Dynamics: Theoretical and Computational Techniques, edited by E.P. Muntz, D.P. Weaver and D.H. Campbell, Vol 118 of Progress in Astronautics and Aeronautics, AIAA, Washington, DC, ISBN 0-930403-55-X, 1989.
15. J.C. Maxwell, Theory of Heat, p. 308: "Tait's Thermodynamics", Nature 17, 257 (1878). Quoted in M. Klein, ref. 4d).
16. J.C. Maxwell, Theory of Heat, p. 308: "Tait's Thermodynamics", Nature 17, 257 (1878). Quoted in M. Klein, ref. 4d).
17. J.C. Maxwell, Theory of Heat, p. 308: "Tait's Thermodynamics", Nature 17, 257 (1878). Quoted in M. Klein, ref. 4d).
18. J.W. Gibbs, Connecticut Academy Transactions 3, 229 (1875), reprinted in The Scientific Papers, 1, 167 Dover, New York 1961);
19. J.W. Gibbs, Connecticut Academy Transactions 3, 229 (1875), reprinted in The Scientific Papers, 1, 167 Dover, New York 1961);
20. L. Boltzmann, Vorlesungen über Gastheorie. 2 vols. Leipzig: Barth, 1896, 1898. This book has been translated into English by S.G. Brush, Lectures on Gas Theory, (Cambridge University Press, London 1964).
21. L. Boltzmann, Vorlesungen über Gastheorie. 2 vols. Leipzig: Barth, 1896, 1898. This book has been translated into English by S.G. Brush, Lectures on Gas Theory, (Cambridge University Press, London 1964).
22. L. Boltzmann, On Zermelo's Paper "On the Mechanical Explanation of Irreversible Processes". Annalen der Physik 60, 392-398 (1897).
23. O. Lanford, Physica A 106, 70 (1981).
24. H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, New York (1991). A. De Masi, E. Presutti, Mathematical Methods for Hydrodynamic Limits, Lecture Notes in Math 1501, Springer-Verlag, New York (1991). J.L. Lebowitz, E. Presutti, H. Spohn, J. Stat. Phys. 51, 841 (1988); R. Esposito and R. Marra, J. Stat. Phys. 74, 981 (1994); C. Landim, C. Kipnis, Scaling Limits for Interacting Particle Systems, Springer-Verlag, Heidelberg, 1998.
25. H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, New York (1991). A. De Masi, E. Presutti, Mathematical Methods for Hydrodynamic Limits, Lecture Notes in Math 1501, Springer-Verlag, New York (1991). J.L. Lebowitz, E. Presutti, H. Spohn, J. Stat. Phys. 51, 841 (1988); R. Esposito and R. Marra, J. Stat. Phys. 74, 981 (1994); C. Landim, C. Kipnis, Scaling Limits for Interacting Particle Systems, Springer-Verlag, Heidelberg, 1998.
26. H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, New York (1991). A. De Masi, E. Presutti, Mathematical Methods for Hydrodynamic Limits, Lecture Notes in Math 1501, Springer-Verlag, New York (1991). J.L. Lebowitz, E. Presutti, H. Spohn, J. Stat. Phys. 51, 841 (1988); R. Esposito and R. Marra, J. Stat. Phys. 74, 981 (1994); C. Landim, C. Kipnis, Scaling Limits for Interacting Particle Systems, Springer-Verlag, Heidelberg, 1998.
27. H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, New York (1991). A. De Masi, E. Presutti, Mathematical Methods for Hydrodynamic Limits, Lecture Notes in Math 1501, Springer-Verlag, New York (1991). J.L. Lebowitz, E. Presutti, H. Spohn, J. Stat. Phys. 51, 841 (1988); R. Esposito and R. Marra, J. Stat. Phys. 74, 981 (1994); C. Landim, C. Kipnis, Scaling Limits for Interacting Particle Systems, Springer-Verlag, Heidelberg, 1998.
28. H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, New York (1991). A. De Masi, E. Presutti, Mathematical Methods for Hydrodynamic Limits, Lecture Notes in Math 1501, Springer-Verlag, New York (1991). J.L. Lebowitz, E. Presutti, H. Spohn, J. Stat. Phys. 51, 841 (1988); R. Esposito and R. Marra, J. Stat. Phys. 74, 981 (1994); C. Landim, C. Kipnis, Scaling Limits for Interacting Particle Systems, Springer-Verlag, Heidelberg, 1998.
29. J.L. Lebowitz and H. Spohn, Communications on Pure and Applied Mathematics, XXXVI, 595, (1983); see in particular section 6(i).
30. L. Boltzmann, Ann. der Physik 57, 773 (1896). Reprinted in 4h).
31. R. P. Feynman, The Character of Physical Law, MIT Press, Cambridge, Mass. (1967), ch. 5.
32. R. Penrose, The Emperor's New Mind, Oxford U.P., New York (1990), ch. 7.
33. Y. Aharonov, P.G. Bergmann and J. L. Lebowitz, Time Symmetry in the Quantum Theory of Measurement, Physical Review 134, B1410 (1964).
34. J. von Neumann (1955) Mathematical Foundations of Quantum Mechanics, pp. 398-416, Princeton Univ. Press, Princeton. Trans, from German ed. (1932: Sprinegr, Berlin) by R. T. Beyer.
35. c.f. R. Griffiths in Physical Origins of Time Asymmetry, J. Haliwell, J. Perez-Mercader and W. Zurech, eds. (Cambridge Univ. Press), 1994.
36. R. Esposito, M. Pulvirenti and A. Teta, The Boltzman Equation for a One-Dimensional Quantum Lorentz Gas, submitted to Communications in Mathematical Physics; L. Erdos and H.-T. Yau, Linear Boltzmann Equation as Scaling Limit of Quantum Lorentz Gas, preprint (1997).
37. R. Esposito, M. Pulvirenti and A. Teta, The Boltzman Equation for a One-Dimensional Quantum Lorentz Gas, submitted to Communications in Mathematical Physics; L. Erdos and H.-T. Yau, Linear Boltzmann Equation as Scaling Limit of Quantum Lorentz Gas, preprint (1997).
38. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge U. P., Cambridge, England (1987).
39. S. Goldstein and J. L. Lebowitz, Quantum Mechanics, in The Physical Review: The First Hundred Years, H. Stroke (ed.), AIP Press, New York, 1995.
40. S. Goldstein, Physics Today, March 1998, p. 42 and April 1998, p. 38.
41. S. Goldstein, Physics Today, March 1998, p. 42 and April 1998, p. 38.
42. D. Dürr, S. Goldstein, N. Zanghi, J. Stat. Phys. 67, 843 (1992); D. Dürr, S. Goldstein, N. Zanghi, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. Cushing, A. Fine, S. Goldstein, eds., Kluwer Academic, Dordrecht, The Netherlands (1996).
43. D. Dürr, S. Goldstein, N. Zanghi, J. Stat. Phys. 67, 843 (1992); D. Dürr, S. Goldstein, N. Zanghi, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. Cushing, A. Fine, S. Goldstein, eds., Kluwer Academic, Dordrecht, The Netherlands (1996).
44. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy, and the Physics of Information, W. Zurek, ed., Addison-Wesley, Reading, Mass. (1990), p. 425; M. Gell-Mann, J. B. Hartler, Phys. Rev. D47, 3345 (1993); M. Gell-Mann, J. B. Hartle, in Proceedings of the 25th International Conference on High Energy Physics, K.K. Phua, Y. Yamaguchi, eds., World Scientific, Singapore (1990).
45. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy, and the Physics of Information, W. Zurek, ed., Addison-Wesley, Reading, Mass. (1990), p. 425; M. Gell-Mann, J. B. Hartler, Phys. Rev. D47, 3345 (1993); M. Gell-Mann, J. B. Hartle, in Proceedings of the 25th International Conference on High Energy Physics, K.K. Phua, Y. Yamaguchi, eds., World Scientific, Singapore (1990).
46. M. Gell-Mann, J. B. Hartle, in Complexity, Entropy, and the Physics of Information, W. Zurek, ed., Addison-Wesley, Reading, Mass. (1990), p. 425; M. Gell-Mann, J. B. Hartler, Phys. Rev. D47, 3345 (1993); M. Gell-Mann, J. B. Hartle, in Proceedings of the 25th International Conference on High Energy Physics, K.K. Phua, Y. Yamaguchi, eds., World Scientific, Singapore (1990).
47. E. Schrödinger, What is Life? and Other Scientifc Essays, Doubleday Anchor Books, Garden City, N.Y., 1965; The Spirit of Science, Sec. 6.
48. E. Schrödinger, What is Life? and Other Scientifc Essays, Doubleday Anchor Books, Garden City, N.Y., 1965; The Spirit of Science, Sec. 6.