Advertisement

The European Physical Journal B

, Volume 79, Issue 1, pp 1–6 | Cite as

Space-time phase transitions in driven kinetically constrained lattice models

  • T. SpeckEmail author
  • J. P. Garrahan
Article

Abstract.

Kinetically constrained models (KCMs) have been widely used to study and understand the origin of glassy dynamics. These models show an ergodic-nonergodic first-order phase transition between phases of distinct dynamical “activity”. We introduce driven variants of two popular KCMs, the FA model and the (2)-TLG, as models for driven supercooled liquids. By classifying trajectories through their entropy production we prove that driven KCMs display an analogous first-order space-time transition between dynamical phases of finite and vanishing entropy production. We discuss how trajectories with rare values of entropy production can be realized as typical trajectories of a mapped system with modified forces.

Keywords

Entropy Production Exit Rate Supercooled Liquid Trajectory Length Entropy Production Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.D. Ediger, C.A. Angell, S.R. Nagel, J. Phys. Chem. 100, 13200 (1996) CrossRefGoogle Scholar
  2. 2.
    P.G. Debenedetti, F.H. Stillinger, Nature 410, 259 (2001) ADSCrossRefGoogle Scholar
  3. 3.
    T.R. Kirkpatrick, D. Thirumalai, P. Wolynes, Phys. Rev. A 40, 1045 (1989) ADSCrossRefGoogle Scholar
  4. 4.
    M. Mézard, G. Parisi, Phys. Rev. Lett. 82, 747 (1999) ADSCrossRefGoogle Scholar
  5. 5.
    J.P. Bouchaud, G. Biroli, J. Chem. Phys. 121, 7347 (2004) ADSCrossRefGoogle Scholar
  6. 6.
    A. Cavagna, Phys. Rep. 476, 51 (2009) ADSCrossRefGoogle Scholar
  7. 7.
    W. Götze, L. Sjögren, Rep. Prog. Phys. 55, 241 (1992) CrossRefGoogle Scholar
  8. 8.
    S.A. Kivelson, G. Tarjus, Nat. Mater. 7, 831 (2008) ADSCrossRefGoogle Scholar
  9. 9.
    D. Chandler, J.P. Garrahan, Annu. Rev. Phys. Chem. 61, 191 (2010) CrossRefGoogle Scholar
  10. 10.
    H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999) ADSCrossRefGoogle Scholar
  11. 11.
    M.D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000) ADSCrossRefGoogle Scholar
  12. 12.
    S.C. Glotzer, J. Non-Cryst. Solids 274, 342 (2000) ADSCrossRefGoogle Scholar
  13. 13.
    R. Richert, J. Phys.: Condens. Matter 14, R703 (2002) ADSCrossRefGoogle Scholar
  14. 14.
    H.C. Andersen, Proc. Natl. Acad. Sci. USA 102, 6686 (2005) ADSCrossRefGoogle Scholar
  15. 15.
    F. Ritort, P. Sollich, Adv. Phys. 52, 219 (2003) ADSCrossRefGoogle Scholar
  16. 16.
    J.P. Garrahan et al., Phys. Rev. Lett. 98, 195702 (2007) ADSCrossRefGoogle Scholar
  17. 17.
    J.P. Garrahan et al., J. Phys. A 42, 075007 (2009) ADSCrossRefMathSciNetGoogle Scholar
  18. 18.
    L.O. Hedges, R.L. Jack, J.P. Garrahan, D. Chandler, Science 323, 1309 (2009) ADSCrossRefGoogle Scholar
  19. 19.
    V. Lecomte, C. Appert-Rolland, F. van Wijland, J. Stat. Phys. 127, 51 (2007) zbMATHADSCrossRefMathSciNetGoogle Scholar
  20. 20.
    M. Baiesi, C. Maes, B. Wynants, Phys. Rev. Lett. 103, 010602 (2009) ADSCrossRefGoogle Scholar
  21. 21.
    J. Hooyberghs, C. Vanderzande, J. Stat. Mech. P02017 (2010) Google Scholar
  22. 22.
    R.L. Jack et al., Phys. Rev. E 78, 011506 (2008) ADSCrossRefGoogle Scholar
  23. 23.
    S.M. Fielding, Phys. Rev. E 66, 016103 (2002) ADSCrossRefGoogle Scholar
  24. 24.
    M. Sellitto, Phys. Rev. Lett. 101, 048301 (2008) ADSCrossRefGoogle Scholar
  25. 25.
    Y. Shokef, A.J. Liu, Europhys. Lett. 90, 26005 (2010) ADSCrossRefGoogle Scholar
  26. 26.
    A.C. Habdas, D. Schaar, E.R. Weeks, Europhys. Lett. 67, 477 (2004) ADSCrossRefGoogle Scholar
  27. 27.
    G.H. Fredrickson, H.C. Andersen, Phys. Rev. Lett. 53, 1244 (1984) ADSCrossRefGoogle Scholar
  28. 28.
    S. Whitelam, L. Berthier, J.P. Garrahan, Phys. Rev. Lett. 92, 185705 (2004) ADSCrossRefGoogle Scholar
  29. 29.
    H. Touchette, Phys. Rep. 478, 1 (2009) ADSCrossRefMathSciNetGoogle Scholar
  30. 30.
    U. Seifert, Phys. Rev. Lett. 95, 040602 (2005) ADSCrossRefGoogle Scholar
  31. 31.
    J.L. Lebowitz, H. Spohn, J. Stat. Phys. 95, 333 (1999) zbMATHCrossRefMathSciNetADSGoogle Scholar
  32. 32.
    G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995) ADSCrossRefGoogle Scholar
  33. 33.
    J. Jackle, K. Kronig, J. Phys.: Condens. Matter 6, 7633 (1994) ADSCrossRefGoogle Scholar
  34. 34.
    A. Pan, J. Garrahan, D. Chandler, Phys. Rev. E 72, 041106 (2005) ADSCrossRefGoogle Scholar
  35. 35.
    P.G. Bolhuis, D. Chandler, C. Dellago, P.L. Geissler, Annu. Rev. Phys. Chem. 53, 291 (2002) ADSCrossRefGoogle Scholar
  36. 36.
    Robert L. Jack, Peter Sollich, Prog. Theor. Phys. Suppl. 184, 304 (2010) zbMATHCrossRefGoogle Scholar
  37. 37.
    A. Baule, R.M.L. Evans, Phys. Rev. Lett. 101, 240601 (2008) ADSCrossRefGoogle Scholar
  38. 38.
    J. Mehl, T. Speck, U. Seifert, Phys. Rev. E 78, 011123 (2008) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of CaliforniaBerkeleyUSA
  2. 2.Chemical Sciences DivisionLawrence Berkeley National LaboratoryBerkeleyUSA
  3. 3.Department of Physics and AstronomyUniversity of NottinghamNottinghamUK

Personalised recommendations