Skip to main content

Non-Monotonic Behavior of the Thermodynamic Work as a Function of Switching Time

Abstract

It is usually believed that the second law necessarily implies the following statement: the faster we drive a system, the larger is the energetic cost for such manipulation. In the present paper, we show that this is not always the case. The energy necessary to drive a system is quantified by the thermodynamic work performed by the external observer. We have shown that there exists a regime in which this quantity reveals a non-monotonic decay as a function of the switching time. Although this effect can be more pronounced in thermally isolated systems, we claim that it can also be present under isothermal conditions. We illustrate our findings with a spin-1/2 in the presence of a time-dependent magnetic field.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2

References

  1. 1.

    T.V. Acconcia, M.V.S. Bonança, Phys. Rev. E. 91, 042141 (2015)

    ADS  Article  Google Scholar 

  2. 2.

    A.E. Allahverdyan, T.M. Nieuvenhuizen, Phys. Rev. E. 75, 051124 (2007)

    ADS  Article  Google Scholar 

  3. 3.

    A.E. Allahverdyan, T.M. Nieuwenhuizen, Phys. Rev. E. 71, 046107 (2005)

    ADS  MathSciNet  Article  Google Scholar 

  4. 4.

    B. Andresen, P. Salamon, R.S. Berry, Phys. Today. 37(9), 62 (1984)

    Article  Google Scholar 

  5. 5.

    E. Aurell, C. Mejía-Monasterio, P. Muratore-Ginanneschi, Phys. Rev. Lett. 106, 250601 (2011)

    ADS  Article  Google Scholar 

  6. 6.

    F. Bloch, Phys. Rev. 70, 460 (1946)

    ADS  Article  Google Scholar 

  7. 7.

    M.V.S. Bonança, S. Deffner, J. Chem. Phys. 140, 244109 (2014)

    ADS  Article  Google Scholar 

  8. 8.

    H.-P. Breuer, F. Petruccione. The theory of open quantum systems (Oxford University Press, London, 2007)

    Book  MATH  Google Scholar 

  9. 9.

    H.B. Callen. Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1985)

    MATH  Google Scholar 

  10. 10.

    M. Campisi, Phys. Rev. E. 78, 051123 (2008)

    ADS  Article  Google Scholar 

  11. 11.

    M. de Koning, J. Chem. Phys. 122, 104106 (2005)

    ADS  Article  Google Scholar 

  12. 12.

    S. Deffner, J. Phys. B: At. Mol. Opt. Phys. 47, 145502 (2014)

    ADS  Article  Google Scholar 

  13. 13.

    A. Fasano, S. Marmi, B. Pelloni. Analytical Mechanics: An Introduction (Oxford University Press, London, 2013)

    MATH  Google Scholar 

  14. 14.

    C. Jarzynski, C. R. Physique. 8, 495–506 (2007)

    ADS  Article  Google Scholar 

  15. 15.

    J.G. Kirkwood, J. Chem. Phys. 14, 180 (1946)

    ADS  Article  Google Scholar 

  16. 16.

    R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)

    ADS  Article  Google Scholar 

  17. 17.

    R. Kubo, M. Toda, N. Hashitsume. Statistical Physics II - Nonequilibrium Statistical Mechanics (Springer, Berlin, 1985)

    MATH  Google Scholar 

  18. 18.

    A. Messiah, Quantum Mechanics, vol. II (North-Holland, Amsterdam, 1976)

  19. 19.

    G. Ruppeiner, Rev. Mod. Phys. 67, 605 (1995)

    ADS  MathSciNet  Article  Google Scholar 

  20. 20.

    P. Salamon, R.S. Berry, Phys. Rev. Lett. 51, 1127 (1983)

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

    T. Schmiedl, U. Seifert, Phys. Rev. Lett. 98, 108301 (2007)

    ADS  Article  Google Scholar 

  22. 22.

    D. Sivak, G.E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)

    ADS  Article  Google Scholar 

  23. 23.

    H. Then, A. Engel, Phys. Rev. E. 77, 041105 (2008)

    ADS  Article  Google Scholar 

  24. 24.

    S. Vaikuntanathan, C. Jarzynski, Europhys. Lett. 87, 60005 (2009)

    ADS  Article  Google Scholar 

  25. 25.

    M. Watanabe, W.P. Reinhardt, Phys. Rev. Lett. 65, 3301 (1990)

    ADS  Article  Google Scholar 

  26. 26.

    F. Weinhold, J. Chem. Phys. 63, 2479 (1975)

    ADS  MathSciNet  Article  Google Scholar 

  27. 27.

    R.M. White. Quantum Theory of Magnetism (Springer, Berlin, 2006)

    Google Scholar 

Download references

Acknowledgments

It is a pleasure to thank T. V. Acconcia and S. Deffner for enriching discussions and the organizers of the Workshop “Quantum Information and Thermodynamics”, São Carlos, Brazil, for the nice meeting we had in February, 2015. The author also acknowledges financial support from FAPESP (Brazil), Project No. 2012/07429-0 and Grant No. 2014/23733-6.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Marcus V. S. Bonança.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bonança, M.V.S. Non-Monotonic Behavior of the Thermodynamic Work as a Function of Switching Time. Braz J Phys 46, 248–253 (2016). https://doi.org/10.1007/s13538-015-0370-7

Download citation

Keywords

  • Nonequilibrium thermodynamics
  • Irreversible processes
  • Second law of thermodynamics