Coarse grains: The emergence of space and order

Foundations of Physics

Volumn 31, Issue 4, 2001, Pages 713-731

  Schulman, L S ^a   Gaveau, Bernard ^b  

^a CLARKSON UNIVERSITY   (United States)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035607909     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017577211902     Document Type: Article

References (21)

1. M Kac, Probability and Related Topics in Physical Sciences, Proceedings of the Summer Seminar, Boulder, Colorado, 1957, with special lectures by G. E. Uhlenbeck, A. R. Hibbs and B. van der Pol (Interscience, London, 1959).
2. For additional objections to coarse graining, see M. C. Mackey, "Microscopic dynamics and the second law of thermodynamics," in Proceedings of the Conference, "Time's Arrows, Quantum Measurements and Superluminal Behavior," Naples, Italy, October 2000, D. Mugnai, A. Ranfagni, and L. S. Schulman, eds. (Italian National Research Council (CNR)). See also M. C. Mackey, Time's Arrow: The Origins of Thermodynamic Behavior (Springer, New York, 1992).
3. For additional objections to coarse graining, see M. C. Mackey, "Microscopic dynamics and the second law of thermodynamics," in Proceedings of the Conference, "Time's Arrows, Quantum Measurements and Superluminal Behavior," Naples, Italy, October 2000, D. Mugnai, A. Ranfagni, and L. S. Schulman, eds. (Italian National Research Council (CNR)). See also M. C. Mackey, Time's Arrow: The Origins of Thermodynamic Behavior (Springer, New York, 1992).
4. H. D. Zeh, The Physical Basis of The Direction of Time, 3rd edn. (Springer, New York, 1999).
5. J. B. Hartle, "Spacetime coarse grainings in nonrelativistic quantum mechanics," Phys. Rev. D 44, 3173 (1991).
6. J. J. Halliwell, "The emergence of hydrodynamic equations from quantum theory: A decoherent histories analysis," Found. Phys. Lett. 39, 1767 (2000).
7. L. S. Schulman, Causality is an effect, in Proceedings of the Conference, "Time's Arrows, Quantum Measurements and Superluminal Behavior," Naples, Italy, October 2000, D. Mugnai, A. Ranfagni and L. S. Schulman, eds. (Italian National Research Council (CNR)).
8. B. Gaveau and L. S. Schulman, "Master equation formulation of non-equilibrium statistical mechanics," J. Math. Phys. 37, 3897 (1996).
9. B. Gaveau and L. S. Schulman, "A general framework for non-equilibrium phenomena: The master equation and its formal consequences," Phys. Lett. A 229, 347 (1997).
10. B. Gaveau and L. S. Schulman, "Theory of non-equilibrium first order phase transitions for stochastic dynamics," J. Math. Phys. 39, 1517 (1998).
11. B. Gaveau, A. Lesne, and L. S. Schulman, "Spectral signatures of hierarchical relaxation. Phys. Lett. A 258, 222 (1999).
12. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd edn., Part 1, pp. 13-14 (1980). Translated by J. B. Sykes and M. J. Kearsley, Course of Theoretical Physics. Vol. 5 (Pergamon, Oxford, 1980).
13. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd edn., Part 1, pp. 13-14 (1980). Translated by J. B. Sykes and M. J. Kearsley, Course of Theoretical Physics. Vol. 5 (Pergamon, Oxford, 1980).
14. yx p0(x).
15. Of course clustering may not occur. In its absence our coarse graining scheme breaks down.
16. l(x) = 0. This would imply linear dependence of the A's in the N-dimensional space that R acts on.
17. A. Friedman, Foundations of Modern Analysis (Dover, New York, 1982).
18. L. J. Schulman, "Clustering for edge-cost minimization," in Proceedings of the 32nd STOC (2000).
19. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th edn. (Academic, New York, 1980).
20. L. S. Schulman, Time's Arrows and Quantum Measurement (Cambridge University Press, Cambridge, 1997).
21. One can carry this perspective to its logical extreme, perhaps leading to a physics analog of the remark of L. Mies van der Rohe, "God is in the details" (New York Herald Tribune, 28 June 1959).