Skip to main content
SpringerLink
Log in

Dynamical entropy and the third law of thermodynamics

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We show that the third law of thermodynamics holds if the equilibrium states cluster appropriately in space and time uniformly for small temperatures. In this case, the entropy density and the dynamical entropy of the shift coincide. As an example in a one-dimensional lattice system with short-range interactions these cluster conditions are verified.

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. KolmogorovA. N., Dokl. Akad. Nauk 119, 861 (1958).

    Google Scholar 

  2. SinaiYu., Dokl. Akad. Nauk 124, 768 (1959).

    Google Scholar 

  3. ConnesA., C. R. Acad. Sci. Paris 301, 1 (1985).

    Google Scholar 

  4. ConnesA., NarnhoferH., and ThirringW., Commun. Math. Phys. 112, 691 (1987).

    Google Scholar 

  5. ConnesA., NarnhoferH., and ThirringW., in H.Mitter and L.Pittner (eds.), Recent Developments in Mathematical Physics, Springer, Berlin, 1987, p. 102.

    Google Scholar 

  6. NarnhoferH. and ThirringW., Lett. Math. Phys. 14, 89 (1987).

    Google Scholar 

  7. Narnhofer, H., Free energy and the dynamical entropy of space translations, submitted to Rep. Math. Phys. (1987).

  8. NarnhoferH. and ThirringW., Fizika 17, 257 (1985).

    Google Scholar 

  9. AizenmanM. and LiebE. H., J. Stat. Phys. 24, 279 (1981).

    Google Scholar 

  10. ThirringW., A Course in Mathematical Physics IV, Springer, New York, 1983.

    Google Scholar 

  11. NarnhoferH., J. Math. Phys. 20, 2502 (1979).

    Google Scholar 

  12. ConnesA. and StörmerE., J. Funct. Anal. 28, 187 (1978).

    Google Scholar 

  13. Narnhofer, H., A new proof of homogeneity of state space of factors of type III1, submitted to RIMS, Kyoto.

  14. RobinsonD. W., Commun. Math. Phys. 7, 337 (1968).

    Google Scholar 

  15. ArakiH., Commun. Math. Phys. 14, 120 (1969).

    Google Scholar 

  16. Hudetz, T., Space-time dynamical entropy of quantum systems, preprint, UWThPh-1988-6 (to appear).

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Wien, Vienna, Austria

    H. Narnhofer & W. Thirring

Authors
  1. H. Narnhofer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Thirring
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work supported in part by ‘Fonds zur Förderung der wissenschaftlichen Forschung in Österreich’, Project No. P6077P.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Narnhofer, H., Thirring, W. Dynamical entropy and the third law of thermodynamics. Lett Math Phys 15, 261–273 (1988). https://doi.org/10.1007/BF00398596

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00398596

Keywords

Search

Navigation