Communications in Mathematical Physics

, Volume 62, Issue 1, pp 35–41 | Cite as

Proof of an entropy conjecture of Wehrl

  • Elliott H. Lieb


Wehrl has proposed a new definition of classical entropy,S, in terms of coherent states and conjectured thatS≧1. A proof of this is given. We discuss the analogous problem for Bloch coherent spin states, but in this case the conjecture is still open. An inequality for the entropy of convolutions is also given.


Entropy Neural Network Statistical Physic Complex System Convolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Wehrl, A.: On the relation between classical and quantum-mechanical entropy. Rept. Math. Phys.Google Scholar
  2. 2.
    Schrödinger, E.: Naturwissenschaften14, 664–666 (1926)Google Scholar
  3. 3.
    Bargmann, V.: Commun. Pure Appl. Math.14, 187–214 (1961);20, 1–101 (1967)Google Scholar
  4. 4.
    Klauder, J. R.: Ann. Phys. (N. Y.)11, 123 (1960)Google Scholar
  5. 5.
    Glauber, R. J.: Phys. Rev.131, 2766 (1963)Google Scholar
  6. 6.
    Lieb, E. H.: Bull. Am. Math. Soc.81, 1–13 (1975)Google Scholar
  7. 7.
    Beckner, W.: Ann. Math.102, 159–182 (1975)Google Scholar
  8. 8.
    Brascamp, H. J., Lieb, E. H.: Advan. Math.20, 151–173 (1976)Google Scholar
  9. 9.
    Radcliffe, J. M.: J. Phys. A4, 313–323 (1971)Google Scholar
  10. 10.
    Kutzner, J.: Phys. Lett. A41, 475–476 (1972)Google Scholar
  11. 11.
    Atkins, P. W., Dobson, J. C.: Proc. Roy. Soc. (London) A321, 321–340 (1971)Google Scholar
  12. 12.
    Arrechi, F. T., Courtens, E., Gilmore, R., Thomas, H.: Phys. Rev. A6, 2211–2237 (1972)Google Scholar
  13. 13.
    Lieb, E. H.: Commun. math. Phys.31, 327–340 (1973)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  1. 1.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

Personalised recommendations