Skip to main content
SpringerLink
Log in

Thermodynamic Anomalies of Small Quantum Systems Within a New Approach to Statistical Physics

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

Based on a new statistical theory, we investigate the thermodynamic anomalies of small quantum systems, such as the negative specific heat (NSH) and negative entropy (NE) within the generalized canonical ensemble. We consider the system–bath heat exchange and “uncompensated heat” in the thermodynamical level which is independent on the details of the system–bath coupling. For ideal finite systems, we calculate two thermodynamic quantities, i.e., the experimental specific heat and the entropy. The results show that the NSH and NE exist in quantum thermodynamics, particularly at low temperatures for small systems. They agree with the results of the reduced partition function theory and reveal that the finite boundary effects of the uncompensated heat and heat exchange of small quantum systems dominate the nonequilibrium irreversible processes.

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

Fig. 1
Fig. 2
Fig. 3

References

  1. H.Y. Tang, J.H. Wang, Y.L. Ma, J. Phys. Soc. Jpn. 83, 064004 (2014)

    Article  Google Scholar 

  2. H.Y. Tang, T.L. Song, J.H. Wang, Y.L. Ma, Chin. Sci. Bull. 59, 2528 (2014)

    Article  Google Scholar 

  3. J. Naudts, Generalized Thermostatistics (Springer, London, 2011)

    Book  Google Scholar 

  4. C. Beck, G.S. Lewis, H.L. Swinney, Phys. Rev. E 63, 035303(R) (2001)

    Article  ADS  Google Scholar 

  5. D.H.E. Gross, Nucl. Phys. A 681, 366 (2001)

    Article  MATH  ADS  Google Scholar 

  6. M. Schmidt, R. Kusche, T. Hippler, J. Donges, W. Kronmüller, B. von Issendorff, H. Haberland, Phys. Rev. Lett. 86, 1191 (2001)

    Article  ADS  Google Scholar 

  7. P.G. Debenedetti, F.H. Stillinger, Nature 410, 259 (2001)

    Article  ADS  Google Scholar 

  8. G.M. Viswanathan, V. Afanasyev, S.V. Buldyrev, E.J. Murphy, H.E. Stanley, Nature (London) 381, 413 (1996)

    Article  ADS  Google Scholar 

  9. F. Serwane, G. Zürn, T. Lompe, T.B. Ottenstein, A.N. Wenz, S. Jochim, Science 332, 336 (2011)

    Article  ADS  Google Scholar 

  10. M. D’Agostino, F. Gulminelli, P. Chomaz, M. Bruno, F. Cannata, R. Bougault, F. Gramegna, I. Iori, L.N. Neindre, G.V. Margagliotti, A. Moroni, G. Vannini, Phys. Lett. B 473, 219 (2000)

  11. F. Gobet, B. Farizon, M. Farizon, M.J. Gaillard, J.P. Buchet, M. Carré, P. Scheier, T.D. Märk, Phys. Rev. Lett. 89, 183403 (2002)

    Article  ADS  Google Scholar 

  12. L. del Rio, J. Åberg, R. Renner, O. Dahlsten, V. Vedral, Nature (London) 474, 61 (2001)

    Article  Google Scholar 

  13. J.H. Wang, Y.L. Ma, Phys. Rev. A 79, 033604 (2009)

    Article  ADS  Google Scholar 

  14. L. Milanovic, H.A. Posch, W. Thirring, Phys. Rev. E 57, 2763 (1998)

    Article  ADS  Google Scholar 

  15. C. Junghans, M. Bachmann, W. Janke, Phys. Rev. Lett. 97, 218103 (2006)

    Article  ADS  Google Scholar 

  16. S. Hilbert, J. Dunkel, Phys. Rev. E 74, 011120 (2006)

    Article  ADS  Google Scholar 

  17. D.H.E. Gross, Microcanonical Thermodynamics (World Scientific, Singapore, 2001)

    Google Scholar 

  18. H.Y. Tang, Y.L. Ma, Phys. Rev. E 83, 061135 (2011)

    Article  ADS  Google Scholar 

  19. M. Campisi, F. Zhan, P. Hänggi, Eur. Phys. Lett. 99, 60004 (2012)

    Article  ADS  Google Scholar 

  20. P. Hänggi, G.-L. Ingold, P. Talkner, New J. Phys. 10, 115008 (2008)

  21. G.-L. Ingold, P. Hänggi, P. Talkner, Phys. Rev. E 79, 061105 (2009)

    Article  ADS  Google Scholar 

  22. M. Campisi, D. Zueco, P. Talkner, Chem. Phys. 375, 187 (2010)

    Article  ADS  Google Scholar 

  23. H. Dong, S. Yang, X.F. Liu, C.P. Sun, Phys. Rev. A 76, 044104 (2007)

    Article  ADS  Google Scholar 

  24. W. Zhang, C.P. Sun, F. Nori, Phys. Rev. E 82, 041127 (2010)

    Article  ADS  Google Scholar 

  25. G.W. Ford, J.T. Lewis, R.F. O’Connell, Ann. Phys. (N.Y.) 185, 270 (1988)

  26. G.W. Ford, R.F. O’Connell, Phys. Rev. B 75, 134301 (2007)

    Article  ADS  Google Scholar 

  27. T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, W. Zwerger, Quantum Transport and Dissipation (Wiley, New York, 1998)

    MATH  Google Scholar 

  28. G.-L. Ingold, Lect. Notes Phys. 611, 1 (2002)

  29. U. Weiss, Quantum Dissipative Systems, 3rd edn. (World Scientific, Singapore, 2008)

    Book  MATH  Google Scholar 

  30. J.-H. Park, S.-W. Kim, Phys. Rev. A 81, 063636 (2010)

    Article  ADS  Google Scholar 

  31. I. Jeon, J.-H. Park, S.-W. Kim, Phys. Rev. A 84, 023636 (2011)

    Article  ADS  Google Scholar 

  32. F. Staniscia, A. Turchi, D. Fanelli, P. H. Chavanis, and G. De Ninno, http://arxiv.org/abs/1003.0631  arXiv:1003.0631 v1 (2010)

  33. J.H. Wang, J.Z. He, Y.L. Ma, Phys. Rev. E 83, 051132 (2011)

    Article  ADS  Google Scholar 

  34. A. Gross, R.D. Levine, Mol. Phys. 105, 419 (2007)

    Article  ADS  Google Scholar 

  35. A. Gross, R.D. Levine, J. Chem. Phys. 125, 144516 (2006)

    Article  ADS  Google Scholar 

  36. I. Prigogine, Introduction to Thermodynamics of Irreversible Processes (Wiley, New York, 1967)

    Google Scholar 

  37. C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. J.C. Reid, E.M. Sevick, D.J. Evans, Europhys. Lett. 72, 726 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  40. D. Ben-Amotz, J.M. Honig, Phys. Rev. Lett. 96, 020602 (2006)

    Article  ADS  Google Scholar 

  41. S. Sasa, http://arxiv.org/abs/1309.7131  arXiv:1309.7131 (2013)

  42. D.M. Harber, J.M. McGuirk, J.M. Obrecht, E.A. Cornell, J. Low Temp. Phys. 133, 229 (2003)

    Article  ADS  Google Scholar 

  43. W. Thirring, Z. Phys. 235, 339 (1970)

    Article  ADS  Google Scholar 

  44. P. Hertel, W. Thirring, Ann. Phys. (N. Y.) 63, 520 (1971)

  45. W. Thirring, H. Narnhofer, H.A. Posch, Phys. Rev. Lett. 91, 130601 (2003)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant no. 11375045 and by the State Key Programs of China under Grant no. 2012CB921604.

Author information

Authors and Affiliations

  1. State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai, 200433, China

    Li Zhou, Hui-yi Tang & Yong-li Ma

Authors
  1. Li Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui-yi Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong-li Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong-li Ma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, L., Tang, Hy. & Ma, Yl. Thermodynamic Anomalies of Small Quantum Systems Within a New Approach to Statistical Physics. J Low Temp Phys 177, 91–98 (2014). https://doi.org/10.1007/s10909-014-1211-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-014-1211-8

Keywords

Search

Navigation