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Irreversibility and spontaneous appearance of coherent behavior in reversible systems

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Abstract.

There is empirical evidence that long time numerical simulations of conservative and reversible partial differential equations evolve, as a general rule (exceptions are the integrable models), towards an equilibrium state that is mainly a coherent structure plus small fluctuations inherent in the conservative and reversible character of the original system. The fluctuations account for the energy difference between the initial configuration and the one of the coherent structure. If the energy is not small enough, then the intrinsic fluctuations may destroy the coherent structure. Thus we arrive to the conclusion that a transition arises from a non-coherent state to a coherent structure as we decrease the initial energy below a critical value. This phenomenon has been successfully observed in various numerical simulations. In this article, we stress that this general behavior is also observed in reversible and conservative cellular automata as in the Q2R model. We point out that this conservative and reversible cellular automata is ab initio deterministic and therefore all our numerical computations are not affected by an approximation of any kind.

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References

  1. V.I. Petviashvili, V.V. Yankov, Rev. Plasma Phys. 14, 5 (1985)

    Google Scholar 

  2. V.E. Zakharov et al., Pis’ma Zh. Eksp. Teor. Fiz. 48, 79 (1988), JETP Lett. 48, 83 (1988)

    ADS  Google Scholar 

  3. S. Dyachenko et al., Zh. Eksp. Teor. Fiz. 96, 2026 (1989), Sov. Phys. JETP 69, 1144 (1989)

    ADS  Google Scholar 

  4. R. Jordan, B. Turkington, C.L. Zirbel, Physica D 137, 353 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. R. Jordan, C. Josserand, Phys. Rev. E 61, 1527 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  6. K. Rasmussen et al., Phys. Rev. Lett. 84, 3740 (2000)

    Article  ADS  Google Scholar 

  7. B. Rumpf, A.C. Newell, Phys. Rev. Lett. 87, 054102 (2001)

    Article  ADS  Google Scholar 

  8. B. Rumpf, A.C. Newell, Physica D 184, 162 (2003)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. C. Josserand, S. Rica, Phys. Rev. Lett. 78, 1215 (1997)

    Article  ADS  Google Scholar 

  10. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005)

    Article  ADS  Google Scholar 

  11. G. Düring, A. Picozzi, S. Rica, Physica D 238, 1524 (2009); see also S. Rica, Équilibre et cinétique des systèmes d’ondes conservatifs, Habilitation à Diriger des Recherches, Université de Pierre et Marie Curie, Paris VI, 2007, http://tel.archives-ouvertes.fr/tel-00222913/fr/

  12. M.J. Davis, S.A. Morgan, K. Burnett, Phys. Rev. Lett. 87, 160402 (2001)

    Article  ADS  Google Scholar 

  13. M.J. Davis, S.A. Morgan, K. Burnett, Phys. Rev. A 66, 053618 (2002)

    Article  ADS  Google Scholar 

  14. Y. Pomeau, Physica D 61, 227 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. S. Dyachenko, A.C. Newell, A. Pushkarev, V.E. Zakharov, Physica D 57, 96 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. T.L. Van Den Berg, D. Fanelli, X. Leoncini, Europhys. Lett. 89, 50010 (2010)

    Article  ADS  Google Scholar 

  17. G. Vichniac, Physica D 10, 96 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  18. Y. Pomeau, J. Phys. A 17, L415 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  19. E. Goles, F. Fogelman, Disc. Appl. Math. 12, 261 (1985)

    Article  MATH  Google Scholar 

  20. E. Goles, G. Vichniac, J. Phys. A 19, L961 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  21. H. Herrmann, J. Statist. Phys. 45, 145 (1986)

    Article  ADS  Google Scholar 

  22. S. Takesue, Phys. Rev. Lett. 59, 2499 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  23. H.J. Herrmann, H.O. Carmesin, D. Stauffer, J. Phys. A 20, 4939 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  24. L. Onsager, Phys. Rev. 65, 117 (1944)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  25. C.N. Yang, Phys. Rev. 85, 808 (1952)

    Article  MATH  ADS  Google Scholar 

  26. V.E. Zakharov, V.S. L’vov, G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, Berlin, 1992)

  27. K. Hasselmann, J. Fluid Mech. 12, 481 (1962)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. K. Hasselmann, J. Fluid Mech. 15, 273 (1963)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. D.J. Benney, P.G. Saffman, Proc. R. Soc. Lond. A 289, 301 (1966)

    Article  ADS  Google Scholar 

  30. A. Newell, S. Nazarenko, L. Biven, Physica D 152-153, 520 (2001)

    Article  ADS  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avda. Diagonal las Torres 2640, Peñalolén, Santiago, Chile

    E. Goles & S. Rica

  2. INLN, CNRS-UNSA, 1361 route des Lucioles, 06560, Valbonne, France

    S. Rica

Authors
  1. E. Goles
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  2. S. Rica
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Correspondence to S. Rica.

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Goles, E., Rica, S. Irreversibility and spontaneous appearance of coherent behavior in reversible systems. Eur. Phys. J. D 62, 127–137 (2011). https://doi.org/10.1140/epjd/e2010-10341-6

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  • DOI: https://doi.org/10.1140/epjd/e2010-10341-6

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