Skip to main content
SpringerLink
Log in

Fluctuation theorems and 1/f noise from a simple matrix

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Here we present a model for a small system combined with an explicit entropy bath that is comparably small. The dynamics of the model is defined by a simple matrix, M. Each row of M corresponds to a macrostate of the system, e.g. net alignment, while the elements in the row represent microstates. The constant number of elements in each row ensures constant entropy, which allows reversible fluctuations, similar to information theory where a constant number of bits allows reversible computations. Many elements in M come from the microstates of the system, but many others come from the bath. Bypassing the bath states yields fluctuations that exhibit standard white noise; whereas with bath states the power spectral density varies as S(f) ∝ 1 /f over a wide range of frequencies, f. Thus, the explicit entropy bath is the mechanism of 1/f noise in this model. Both forms of the model match Crooks’ fluctuation theorem exactly, indicating that the theorem applies not only to infinite reservoirs, but also to finite-sized baths. The model is used to analyze measurements of 1/f-like noise from a sub-micron tunnel junction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G.E. Crooks, Phys. Rev. E 60, 2721 (1999)

    Article  ADS  Google Scholar 

  2. D.J. Evans, E.G.D. Cohen, G.P. Morriss, Phys. Rev. Lett. 71, 2401 (1993)

    Article  ADS  Google Scholar 

  3. G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)

    Article  ADS  Google Scholar 

  4. R. Kawai, J.M.R. Parrondo, C. Van den Broek, Phys. Rev. Lett. 98, 080602 (2007)

    Article  ADS  Google Scholar 

  5. S. Pressé, K. Ghosh, J. Lee, K.A. Dill, Rev. Mod. Phys. 85, 1115 (2013)

    Article  ADS  Google Scholar 

  6. D. Collin, F. Ritort, C. Jarzynski, S.B. Smith, I. Tinoco Jr., C. Bustamante, Nature 437, 231 (2005)

    Article  ADS  Google Scholar 

  7. S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, M. Sano, Nat. Phys. 6, 988 (2010)

    Article  Google Scholar 

  8. G. Verley, M. Esposito, T. Willaert, C. Van den Broeck, Nat. Commun. 5, 1 (2014)

    Article  Google Scholar 

  9. A. Berut, A. Arkakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, E. Lutz, Nature 483, 187 (2012)

    Article  ADS  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. J. Mehl, B. Lander, C. Bechinger, V. Blickle, U. Seifert, Phys. Rev. Lett. 108, 220601 (2012)

    Article  ADS  Google Scholar 

  12. T.L. Hill, Thermodynamics of Small Systems (Parts I and II) (Dover, Mineola NY, 1994)

  13. R.V. Chamberlin, Nature 408, 337 (2000)

    Article  ADS  Google Scholar 

  14. R.V. Chamberlin, J.V. Vermaas, G.H. Wolf, Eur. Phys. J. B 71, 1 (2009)

    Article  ADS  Google Scholar 

  15. R.V. Chamberlin, Entropy 17, 52 (2015)

    Article  ADS  Google Scholar 

  16. C.T. Rogers, R.A. Buhrman, Phys. Rev. Lett. 53, 1272 (1984)

    Article  ADS  Google Scholar 

  17. R. Landauer, Phys. Today 44, 23 (1991)

    Article  ADS  Google Scholar 

  18. R.P. Feynman, Found. Phys. 16, 507 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  19. R.P. Feynman, Statistical Mechanics (Perseus Books, Reading, 1998)

  20. U. Seifert, Rep. Prog. Phys. 75, 1 (2012)

    Article  Google Scholar 

  21. R.V. Chamberlin, D.M. Nasir, Phys. Rev. E 90, 012142 (2014)

    Article  ADS  Google Scholar 

  22. S. Kogan, Electronic Noise and Fluctuations in Solids (Cambridge University Press, Cambridge, 2008)

  23. E. Vidal Russell, N.E. Israeloff, Nature 408, 695 (2000)

    Article  ADS  Google Scholar 

  24. F. Yoshihara, K. Harrabi, A.O. Niskanen, Y. Nakamura, J.S. Tsai, Phys. Rev. Lett. 97, 167001 (2006)

    Article  ADS  Google Scholar 

  25. A.A. Balandin, Nat. Nanotechnol. 8, 549 (2013)

    Article  ADS  Google Scholar 

  26. E. Paladino, Y.M. Galperin, G. Falci, B.L. Altshuler, Rev. Mod. Phys. 86, 361 (2014)

    Article  ADS  Google Scholar 

  27. K.S. Nagapriya, A.K. Raychaudhuri, Phys. Rev. Lett. 96, 038102 (2006)

    Article  ADS  Google Scholar 

  28. R.M.M. Smeets, U.F. Keyser, N.H. Dekker, C. Dekker, Proc. Natl. Acad. Sci. USA 105, 417 (2008)

    Article  ADS  Google Scholar 

  29. J.P. Boon, Adv. Complex Syst. 13, 155 (2010)

    Article  MathSciNet  Google Scholar 

  30. L.M. Ward, P.E. Greenwood, http://www.scholarpedia.org/article/1/f˙noise

  31. R.V. Chamberlin, G.H. Wolf, Eur. Phys. J. B 67, 495 (2009)

    Article  ADS  Google Scholar 

  32. R.V. Chamberlin, Physica A 391, 5384 (2012)

    Article  ADS  Google Scholar 

  33. G.M. Wang, E.M. Sevick, E. Mittag, D.J. Searles, D.J. Evans, Phys. Rev. Lett. 89, 050601 (2002)

    Article  ADS  Google Scholar 

  34. J.L. Lebowitz, Phys. Today 46, 32 (1993)

    Article  Google Scholar 

  35. D.A. Lavis, Phil. Sci. 75, 682 (2008)

    Article  MathSciNet  Google Scholar 

  36. R.H. Koch, D.P. DiVincenzo, J. Clarke, Phys. Rev. Lett. 98, 267003 (2007)

    Article  ADS  Google Scholar 

  37. L. Faoro, L.B. Ioffe, Phys. Rev. Lett. 100, 227005 (2008)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Arizona State University, Tempe, AZ, 85287-1504, USA

    Ralph V. Chamberlin, Bryce F. Davis & Andrew S.H. Shevchuk

  2. Department of Physical Engineering, Mie University, 514-8507, Mie, Japan

    Sumiyoshi Abe

  3. Institute of Physics, Kazan Federal University, 420008, Kazan, Russia

    Sumiyoshi Abe

  4. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Priscilla E. Greenwood

Authors
  1. Ralph V. Chamberlin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sumiyoshi Abe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bryce F. Davis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Priscilla E. Greenwood
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Andrew S.H. Shevchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ralph V. Chamberlin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chamberlin, R., Abe, S., Davis, B. et al. Fluctuation theorems and 1/f noise from a simple matrix. Eur. Phys. J. B 89, 185 (2016). https://doi.org/10.1140/epjb/e2016-70242-0

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2016-70242-0

Keywords

Search

Navigation