The European Physical Journal Special Topics

, Volume 226, Issue 3, pp 365–371 | Cite as

Reducing low-frequency noise during reversible fluctuations

Regular Article
  • 36 Downloads
Part of the following topical collections:
  1. Nonlinearity, Nonequilibrium and Complexity: Questions and Perspectives in Statistical Physics

Abstract

The noise from most materials exhibits a power-spectral density that tends to diverge as S(f) ∝ 1/f at low frequencies, f. A fundamental mechanism for this 1/f noise comes from the thermodynamics of small systems applied to reversible fluctuations of nanometer-sized regions inside bulk samples. Here this “nanothermodynamics” is used to derive a nonlinear correction to Boltzmann’s factor. Specifically: Boltzmann’s factor comes from the first-order (linear) derivative of entropy with respect to energy, whereas the nonlinear correction comes from higher-order terms. The nonlinear correction is applied to Monte Carlo simulations of small regions in the Ising model, yielding a low-frequency crossover to white noise that keeps the power-spectral density finite as f → 0. It is shown that the low-frequency noise in the model is reduced by reducing the size of the regions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C.T. Rogers, R.A. Buhrman, Phys. Rev. Lett. 53, 1272 (1984)ADSCrossRefGoogle Scholar
  2. 2.
    E. Vidal Russell, N.E. Israeloff, Nature 408, 695 (2000)ADSCrossRefGoogle Scholar
  3. 3.
    D. Collin, F. Ritort, C. Jarzynski, S.B. Smith, I. Tinoco Jr, C. Bustamante, Nature 437, 231 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, M. Sano, Nat. Phys. 6, 988 (2010)CrossRefGoogle Scholar
  5. 5.
    J. Mehl, B. Lander, C. Bechinger, V. Blickle, U. Seifert, Phys. Rev. Lett. 108, 220601 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    A. Berut, A. Arkakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, E. Lutz, Nature 483, 187 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    J.V. Koski, T. Sagawa, O.P. Saira, Y. Yoon, A. Kutvonen, P. Solinas, M. Möttönen, T. Ala-Nissila, J.P. Pekola, Nat. Phys. 9, 644 (2013)CrossRefGoogle Scholar
  8. 8.
    G. Verley, M. Esposito, T. Willaert, C. Van den Broeck, Nat. Comm. 5, 1 (2014)CrossRefGoogle Scholar
  9. 9.
    G.E. Crooks, Phys. Rev. E 60, 2721 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    D.J. Evans, E.G.D. Cohen, G.P. Morriss, Phys. Rev. Lett. 71, 2401 (1993)ADSCrossRefGoogle Scholar
  11. 11.
    G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    R. Kawai, J.M.R. Parrondo, C. Van den Broek, Phys. Rev. Lett. 98, 080602 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    S. Pressé, K. Ghosh, J. Lee, K.A. Dill, Rev. Mod. Phys. 85, 1115 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    U. Seifert, Rep. Prog. Phys. 75, 1 (2012)CrossRefGoogle Scholar
  15. 15.
    E.G.D. Cohen, D. Mauzerall, J. Stat. Mech: Theor. Exp. 2004, P07006 (2004)CrossRefGoogle Scholar
  16. 16.
    C. Jarzynski, J. Stat. Mech: Theor. Exp. 2004, P09005 (2004)CrossRefGoogle Scholar
  17. 17.
    R.P. Feynman, Statistical Mechanics (Westview Press, Boulder, CO, 1998)Google Scholar
  18. 18.
    E. Donth, J. Non-Cryst. Solids 53, 325 (1982)ADSCrossRefGoogle Scholar
  19. 19.
    V.I. Yukalov, Phys. Rep. 208, 395 (1991)ADSCrossRefGoogle Scholar
  20. 20.
    R. Böhmer, R.V. Chamberlin, G. Diezemann, B. Geil, A. Heuer, G. Hinze, S.C. Kuebler, R. Richert, B. Schiener, H. Sillescu, H.W. Spiess, U. Tracht, M. Wilhelm, J. Non-Cryst. Solids 235, 1 (1998)CrossRefGoogle Scholar
  21. 21.
    M.D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000)ADSCrossRefGoogle Scholar
  22. 22.
    R. Richert, J. Phys.: Condens. Matter 14, R703 (2002)ADSGoogle Scholar
  23. 23.
    S.A. Reinsberg, A. Heuer, B. Doliwa, H. Zimmermann, H.W. Spiess, J. Non-Cryst. Sol. 307, 208 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    L.J. Kaufman, Annu. Rev. Phys. Chem. 64, 177 (2013)ADSCrossRefGoogle Scholar
  25. 25.
    M. Meissner, K. Spitzmann, Phys. Rev. Lett. 46, 265 (1981)ADSCrossRefGoogle Scholar
  26. 26.
    P.K. Dixon, S.R. Nagel, Phys. Rev. Lett. 61, 341 (1988)ADSCrossRefGoogle Scholar
  27. 27.
    R.V. Chamberlin, B. Schiener, R. Böhmer, MRS Bulletin 455, 117 (1997)CrossRefGoogle Scholar
  28. 28.
    R.V. Chamberlin, Phase Transitions 65, 169 (1998)CrossRefGoogle Scholar
  29. 29.
    R.V. Chamberlin, Phys. Rev. Lett. 83, 5134 (1999)ADSCrossRefGoogle Scholar
  30. 30.
    R. Richert, S. Weinstein, Phys. Rev. Lett. 97, 095703 (2006)ADSCrossRefGoogle Scholar
  31. 31.
    T.L. Hill, Thermodynamics of Small Systems (Parts I and II) (Dover, Mineola, NY, 1994)Google Scholar
  32. 32.
    R.V. Chamberlin, Nature 408, 337 (2000)ADSCrossRefGoogle Scholar
  33. 33.
    R.V. Chamberlin, J.V. Vermaas, G.H. Wolf, Eur. Phys. J. B 71, 1 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    R.V. Chamberlin, Entropy 17, 52 (2015)ADSCrossRefGoogle Scholar
  35. 35.
    J.B. Johnson, Phys. Rev. 26, 71 (1925)ADSCrossRefGoogle Scholar
  36. 36.
    S. Kogan, Electronic Noise and Fluctuations in Solids (Cambridge University Press, Cambridge, 2008)Google Scholar
  37. 37.
    F. Yoshihara, K. Harrabi, A.O. Niskanen, Y. Nakamura, J.S. Tsai, Phys. Rev. Lett. 97, 167001 (2006)ADSCrossRefGoogle Scholar
  38. 38.
    A.A. Balandin, Nature Nanotechnology 8, 549 (2013)ADSCrossRefGoogle Scholar
  39. 39.
    E. Paladino, Y.M. Galperin, G. Falci, B.L. Altshuler, Rev. Mod. Phys. 86, 361 (2014)ADSCrossRefGoogle Scholar
  40. 40.
    K.S. Nagapriya, A.K. Raychaudhuri, Phys. Rev. Lett. 96, 038102 (2006)ADSCrossRefGoogle Scholar
  41. 41.
    R.M.M. Smeets, U.F. Keyser, N.H. Dekker, C. Dekker, Proc. Natl. Acad. Sci. U.S.A. 105, 417 (2008)ADSCrossRefGoogle Scholar
  42. 42.
    J.P. Boon, Adv. Complex Syst. 13, 155 (2010)MathSciNetCrossRefGoogle Scholar
  43. 43.
  44. 44.
    R.V. Chamberlin, D.M. Nasir, Phys. Rev. E 90, 012142 (2014)ADSCrossRefGoogle Scholar
  45. 45.
    R.V. Chamberlin, G.H. Wolf, Eur. Phys. J. B 67, 495 (2009)ADSCrossRefGoogle Scholar
  46. 46.
    R.V. Chamberlin, Physica A 391, 5384 (2012)ADSCrossRefGoogle Scholar
  47. 47.
    R.V. Chamberlin, B.F. Davis, Phys. Rev. E 88, 042108 (2013)ADSCrossRefGoogle Scholar
  48. 48.
    H.M. James, E. Guth, J. Chem. Phys. 11, 455 (1943)ADSCrossRefGoogle Scholar
  49. 49.
    R.P. Feynman, R.B. Leighton, M. Sands, Lectures on Physics (Pearson Addison Wesley, San Francisco, 2006), Vol. 1, p. 44Google Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Department of PhysicsArizona State UniversityTempe, AZUSA

Personalised recommendations