Lyapunov exponents and the extensivity of dimensional loss for systems in thermal gradients

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 5 2, 2003, Pages 562041-5620416

  Aoki, Kenichiro ^a   Kusnezov, Dimitri ^b  

^a KEIO UNIVERSITY   (Japan)

^b YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; ENTROPY; LYAPUNOV METHODS; MATHEMATICAL MODELS; THERMAL GRADIENTS; THERMODYNAMICS; TRANSPORT PROPERTIES;

BULK BEHAVIOR; THERMAL EQUILIBRIUM;

STATISTICAL MECHANICS;

EID: 0942278441     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. W.G. Hoover, Computational Statistical Mechanics (Elsevier, Amsterdam, 1991); D.J. Evans and G.P. Morriss, Statistical Mechanics of Non-Equilibrium Liquids (Academic, London, 1990); P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge, New York, 1998).
2. W.G. Hoover, Computational Statistical Mechanics (Elsevier, Amsterdam, 1991); D.J. Evans and G.P. Morriss, Statistical Mechanics of Non-Equilibrium Liquids (Academic, London, 1990); P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge, New York, 1998).
3. W.G. Hoover, Computational Statistical Mechanics (Elsevier, Amsterdam, 1991); D.J. Evans and G.P. Morriss, Statistical Mechanics of Non-Equilibrium Liquids (Academic, London, 1990); P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge, New York, 1998).
4. P. Gaspard and G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990).
5. N.I. Chernov, G.L. Eyink, J.L. Lebowitz, and Ya.G. Sinai, Phys. Rev. Lett. 70, 2209 (1993)
6. H.A. Posch and W.G. Hoover, Phys. Rev. E 58, 4344 (1998)
7. D.J. Evans, E.G.D. Cohen, D.J. Searles, and F. Bonetto, J. Stat. Phys. 101, 17 (2000)
8. B. Holian, W. Hoover, and H. Posch, Phys. Rev. Lett. 59, 10 (1987).
9. D. Barnett, et al., Phys. Rev. Lett. 76, 1812 (1996); R. van Zon, H. van Beijeren, and Ch. Dellago, ibid. 80, 2035 (1998); A. Latz, H. van Beijeren, and J.R. Dorfman, ibid. 78, 207 (1997).
10. D. Barnett, et al., Phys. Rev. Lett. 76, 1812 (1996); R. van Zon, H. van Beijeren, and Ch. Dellago, ibid. 80, 2035 (1998); A. Latz, H. van Beijeren, and J.R. Dorfman, ibid. 78, 207 (1997).
11. D. Barnett, et al., Phys. Rev. Lett. 76, 1812 (1996); R. van Zon, H. van Beijeren, and Ch. Dellago, ibid. 80, 2035 (1998); A. Latz, H. van Beijeren, and J.R. Dorfman, ibid. 78, 207 (1997).
12. H.A. Posch and W.G. Hoover, Phys. Rev. A 38, 473 (1988); B. Moran, W.G. Hoover, and S. Bestiale, J. Stat. Phys. 48, 709 (1987)
13. H.A. Posch and W.G. Hoover, Phys. Rev. A 38, 473 (1988); B. Moran, W.G. Hoover, and S. Bestiale, J. Stat. Phys. 48, 709 (1987)
14. W.G. Hoover and H.A. Posch, Phys. Rev. E 49, 1913 (1994)
15. G.P. Morriss, Phys. Lett. A 134, 307 (1989); D.J. Evans, E.G.D. Cohen, and G.P. Morriss, Phys. Rev. A 42, 5990 (1990)
16. G.P. Morriss, Phys. Lett. A 134, 307 (1989); D.J. Evans, E.G.D. Cohen, and G.P. Morriss, Phys. Rev. A 42, 5990 (1990)
17. H. van Beijeren et al., Phys. Rev. Lett. 77, 1974 (1996); P. Gaspard et al., ibid. 86, 1506 (2001).
18. H. van Beijeren et al., Phys. Rev. Lett. 77, 1974 (1996); P. Gaspard et al., ibid. 86, 1506 (2001).
19. M.E. Tuckerman, C.J. Mundy, and M.L. Klein, Phys. Rev. Lett. 78, 2042 (1997); 80, 4105 (1998); W.G. Hoover et al., ibid. 80, 4103 (1998); P. Reimann, ibid. 80, 4104 (1998); W-J. Tzeng and C-C. Chen, Phys. Lett. A 246, 52 (1998); C. Wagner, R. Klages, and G. Nicolis, Phys. Rev. E 60, 1401 (1999); W.G. Hoover, Phys. Lett. A 255, 37 (1999).
20. M.E. Tuckerman, C.J. Mundy, and M.L. Klein, Phys. Rev. Lett. 78, 2042 (1997); 80, 4105 (1998); W.G. Hoover et al., ibid. 80, 4103 (1998); P. Reimann, ibid. 80, 4104 (1998); W-J. Tzeng and C-C. Chen, Phys. Lett. A 246, 52 (1998); C. Wagner, R. Klages, and G. Nicolis, Phys. Rev. E 60, 1401 (1999); W.G. Hoover, Phys. Lett. A 255, 37 (1999).
21. M.E. Tuckerman, C.J. Mundy, and M.L. Klein, Phys. Rev. Lett. 78, 2042 (1997); 80, 4105 (1998); W.G. Hoover et al., ibid. 80, 4103 (1998); P. Reimann, ibid. 80, 4104 (1998); W-J. Tzeng and C-C. Chen, Phys. Lett. A 246, 52 (1998); C. Wagner, R. Klages, and G. Nicolis, Phys. Rev. E 60, 1401 (1999); W.G. Hoover, Phys. Lett. A 255, 37 (1999).
22. M.E. Tuckerman, C.J. Mundy, and M.L. Klein, Phys. Rev. Lett. 78, 2042 (1997); 80, 4105 (1998); W.G. Hoover et al., ibid. 80, 4103 (1998); P. Reimann, ibid. 80, 4104 (1998); W-J. Tzeng and C-C. Chen, Phys. Lett. A 246, 52 (1998); C. Wagner, R. Klages, and G. Nicolis, Phys. Rev. E 60, 1401 (1999); W.G. Hoover, Phys. Lett. A 255, 37 (1999).
23. M.E. Tuckerman, C.J. Mundy, and M.L. Klein, Phys. Rev. Lett. 78, 2042 (1997); 80, 4105 (1998); W.G. Hoover et al., ibid. 80, 4103 (1998); P. Reimann, ibid. 80, 4104 (1998); W-J. Tzeng and C-C. Chen, Phys. Lett. A 246, 52 (1998); C. Wagner, R. Klages, and G. Nicolis, Phys. Rev. E 60, 1401 (1999); W.G. Hoover, Phys. Lett. A 255, 37 (1999).
24. M.E. Tuckerman, C.J. Mundy, and M.L. Klein, Phys. Rev. Lett. 78, 2042 (1997); 80, 4105 (1998); W.G. Hoover et al., ibid. 80, 4103 (1998); P. Reimann, ibid. 80, 4104 (1998); W-J. Tzeng and C-C. Chen, Phys. Lett. A 246, 52 (1998); C. Wagner, R. Klages, and G. Nicolis, Phys. Rev. E 60, 1401 (1999); W.G. Hoover, Phys. Lett. A 255, 37 (1999).
25. M.E. Tuckerman, C.J. Mundy, and M.L. Klein, Phys. Rev. Lett. 78, 2042 (1997); 80, 4105 (1998); W.G. Hoover et al., ibid. 80, 4103 (1998); P. Reimann, ibid. 80, 4104 (1998); W-J. Tzeng and C-C. Chen, Phys. Lett. A 246, 52 (1998); C. Wagner, R. Klages, and G. Nicolis, Phys. Rev. E 60, 1401 (1999); W.G. Hoover, Phys. Lett. A 255, 37 (1999).
26. K. Aoki and D. Kusnezov, Phys. Lett. B 477, 348 (2000); Ann. Phys. 295, 50 (2002).
27. K. Aoki and D. Kusnezov, Phys. Lett. B 477, 348 (2000); Ann. Phys. 295, 50 (2002).
28. K. Aoki and D. Kusnezov, Phys. Lett. A 265, 250 (2000).
29. R. Livi, A. Politi, S. Ruffo, and A. Vulpiani J. Stat. Phys. 46, 147 (1987); W.G. Hoover and H.A. Posch, Phys. Rev. E 51, 273 (1995); C. Dellago and H.A. Posch, Physica A 240, 68 (1997); D. Searles, D.J. Evans, and D.J. Isibister, ibid. 240, 96 (1997).
30. R. Livi, A. Politi, S. Ruffo, and A. Vulpiani J. Stat. Phys. 46, 147 (1987); W.G. Hoover and H.A. Posch, Phys. Rev. E 51, 273 (1995); C. Dellago and H.A. Posch, Physica A 240, 68 (1997); D. Searles, D.J. Evans, and D.J. Isibister, ibid. 240, 96 (1997).
31. R. Livi, A. Politi, S. Ruffo, and A. Vulpiani J. Stat. Phys. 46, 147 (1987); W.G. Hoover and H.A. Posch, Phys. Rev. E 51, 273 (1995); C. Dellago and H.A. Posch, Physica A 240, 68 (1997); D. Searles, D.J. Evans, and D.J. Isibister, ibid. 240, 96 (1997).
32. R. Livi, A. Politi, S. Ruffo, and A. Vulpiani J. Stat. Phys. 46, 147 (1987); W.G. Hoover and H.A. Posch, Phys. Rev. E 51, 273 (1995); C. Dellago and H.A. Posch, Physica A 240, 68 (1997); D. Searles, D.J. Evans, and D.J. Isibister, ibid. 240, 96 (1997).
33. K. Aoki and D. Kusnezov, Phys. Rev. Lett. 86, 4029 (2001).
34. B. Hu and B. Li, H. Zhao, Phys. Rev. E 61, 3828 (2000)
35. H.A. Posch and W.G. Hoover, Phys. Lett. 113A, 82 (1985); I. Goldhirsch, P-L. Sulem, and S.A. Orszag, Physica D 27, 311 (1987)
36. H.A. Posch and W.G. Hoover, Phys. Lett. 113A, 82 (1985); I. Goldhirsch, P-L. Sulem, and S.A. Orszag, Physica D 27, 311 (1987)
37. K. Aoki and D. Kusnezov, Phys. Lett. A 309, 377 (2003).