Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Entropy inequalities

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

Abstract

Some inequalities and relations among entropies of reduced quantum mechanical density matrices are discussed and proved. While these are not as strong as those available for classical systems they are nonetheless powerful enough to establish the existence of the limiting mean entropy for translationally invariant states of quantum continuous systems.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Ruelle, D.: Statistical mechanics. Proposition (7.2.6). New York: W. A. Benjamin 1969. For related results the reader is referred to: A. Huber in “Mathematical Methods in Solid State and Superfluid Theory”, R. C. Clark and G. H. Derrick ed., Oliver and Boyd, Edinburgh, 1969, page 364; H. Falk, “Inequalities of J. W. Gibbs” to appear in Amer. J. Phys., July, 1970.

    Google Scholar 

  2. Lanford, O. E., Robinson, D. W.: J. Math. Phys.9, 1120–1125 (1968). Partial results have been obtained by F. Baumann and R. Jost, Problems of theoretical physics. Essays dedicated to N. N. Bogoliubov, p. 285. Moscow: Nauka 1969.

    Google Scholar 

  3. Ruelle, D.:op. cit., Proposition (2.5.4).

    Google Scholar 

  4. ——op. cit., Proposition (2.5.2).

    Google Scholar 

  5. Golden, S.: Phys. Rev.137, B1127 (1965); — C. Thompson, J. Math. Phys.6, 1812 (1965).

  6. Ruelle, D.:op. cit., Proposition (7.2.10) and Section (7.2.13). See also H. Falk and E. Adler, Phys. Rev.168, 185–187 (1968); L. W. Bruch and H. Falk, “Gibbs Inequality in Quantum Statistical Mechanics” to appear in Phys. Rev.

  7. Araki, H., Woods, E. J.: Publ. Res. Inst. Math. Sci. Kyoto Univ. Ser. A,2, 157–242 (1966). Definition 2.1.

    Google Scholar 

  8. Ruelle, D.:op. cit., Section (7.2.13).

    Google Scholar 

  9. Miracle-Sole, S., Robinson, D. W.: Commun. Math. Phys.14, 235–270 (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Huzihiro Araki

  2. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts, USA

    Elliott H. Lieb

Authors
  1. Huzihiro Araki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elliott H. Lieb
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work supported by National Science Foundation Grant GP-9414.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Araki, H., Lieb, E.H. Entropy inequalities. Commun.Math. Phys. 18, 160–170 (1970). https://doi.org/10.1007/BF01646092

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01646092

Keywords

Search

Navigation