On asymptotic behavior of work distributions for driven Brownian motion

  • Viktor Holubec
  • Dominik Lips
  • Artem Ryabov
  • Petr Chvosta
  • Philipp Maass
Regular Article

Abstract

We propose a simple conjecture for the functional form of the asymptotic behavior of work distributions for driven overdamped Brownian motion of a particle in confining potentials. This conjecture is motivated by the fact that these functional forms are independent of the velocity of the driving for all potentials and protocols, where explicit analytical solutions for the work distributions have been derived in the literature. To test the conjecture, we use Brownian dynamics simulations and a recent theory developed by Engel and Nickelsen (EN theory), which is based on the contraction principle of large deviation theory. Our tests suggest that the conjecture is valid for potentials with a confinement equal to or weaker than the parabolic one, both for equilibrium and for nonequilibrium distributions of the initial particle position. For potentials with stronger confinement, the conjecture fails and gives a good approximate description only for fast driving. In addition we obtain a new analytical solution for the asymptotic behavior of the work distribution for the V-potential by application of the EN theory, and we extend this theory to nonequilibrated initial particle positions.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    U. Seifert, Rep. Prog. Phys. 75, 126001 (2012)ADSCrossRefGoogle Scholar
  2. 2.
    F. Ritort, Adv. Chem. Phys. 137, 31 (2008)Google Scholar
  3. 3.
    C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)ADSCrossRefGoogle Scholar
  4. 4.
    G.E. Crooks, Phys. Rev. E 60, 2721 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    U. Seifert, Phys. Rev. Lett. 95, 040602 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    M. Esposito, C. Van den Broeck, Phys. Rev. E 82, 011143 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    C. Van den Broeck, M. Esposito, Phys. Rev. E 82, 011144 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    G.N. Bochkov, Y.E. Kuzovlev, Physics-Uspekhi 56, 590 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    M. Palassini, F. Ritort, Phys. Rev. Lett. 107, 060601 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    T. Speck, U. Seifert, Phys. Rev. E 70, 066112 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    A. Engel, Phys. Rev. E 80, 021120 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    D. Nickelsen, A. Engel, Eur. Phys. J. B 82, 207 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer-Verlag, 1985)Google Scholar
  14. 14.
    A. Ryabov, M. Dierl, P. Chvosta, M. Einax, P. Maass, J. Phys. A 46, 075002 (2013)ADSCrossRefMathSciNetGoogle Scholar
  15. 15.
    D. Nickelsen, Ph.D. thesis (in German), Carl von Ossietzky Universität Oldenburg, Germany, 2012Google Scholar
  16. 16.
    C. Kwon, J.D. Noh, H. Park, Phys. Rev. E 88, 062102 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    O. Mazonka, C. Jarzynski, arXiv:cond-mat/9912121 (1999)
  18. 18.
    T. Speck, J. Phys. A 44, 305001 (2011)ADSCrossRefMathSciNetGoogle Scholar
  19. 19.
    Y. Saito, T. Mitsui, Ann. Inst. Stat. Math. 45, 419 (1993)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods (Wiley-Interscience, New York, 1987)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Viktor Holubec
    • 1
  • Dominik Lips
    • 2
  • Artem Ryabov
    • 1
  • Petr Chvosta
    • 1
  • Philipp Maass
    • 2
  1. 1.Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular PhysicsPrahaCzech Republic
  2. 2.Universität OsnabrückOsnabrückGermany

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