International Journal of Theoretical Physics

, Volume 29, Issue 12, pp 1379–1392 | Cite as

Underlying probability distributions of Planck's radiation law

  • B. H. Lavenda


The derivation of Planck's radiation law can be considered as a transformation of a thermodynamic relation for black-body radiation into a fundamental relation in which the error law is the negative binomial distribution. In both limiting frequency ranges it transforms into Poisson distributions; in the Wien limit, it is the distribution of the number of photons, whose most probable value is given by Boltzmann's expression, while in the Rayleigh-Jeans limit, it is the distribution of the number of Planck oscillators. In the general case, they are Bernoullian random variables. In the Rayleigh-Jeans limit, the probability of determining the number of oscillators in a given frequency interval for a fixed value of the energy can be inverted to determining the probability of the energy for a fixed number of oscillators. The probability density is that of the canonical ensemble.


Probability Distribution Field Theory Probability Density Elementary Particle Quantum Field Theory 
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. Blanc-Lapierre, A., and Tortat, A. (1956). InProceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. III, University of California Press, Berkeley, pp. 145–170.Google Scholar
  2. Brillouin, L. (1962).Science and Information Theory, 2nd ed., Academic Press, New York, p. 189.Google Scholar
  3. Ehrenfest, P., and Kamerlingh Onnes, H. (1914).Proceedings Academy of Amsterdam,17, 870.Google Scholar
  4. Einstein, A. (1905).Annalen der Physik,17, 132 [transi., A. B. Arons and M. B. Peppard,American Journal of Physics,33, 367 (1965)].Google Scholar
  5. Gibbs, J. W. (1902).Elementary Principles in Statistical Mechanics, Yale University Press, New Haven, p. 23.Google Scholar
  6. Klein, M. J. (1977). InHistory of Twentieth Century Physics, Academic Press, New York, pp. 1–39.Google Scholar
  7. Lavenda, B. H. (1988).International journal of Theoretical Physics,27, 1371.Google Scholar
  8. Lavenda, B. H., and Dunning-Davies, J. (1990a).International Journal of Theoretical Physics,29, 85.Google Scholar
  9. Lavenda, B. H., and Dunning-Davies, J. (1990b).International Journal of Theoretical Physics,29, 509.Google Scholar
  10. Lavenda, B. H., and Dunning-Davies, J. (1991). Entropy paradoxes, submitted for publication.Google Scholar
  11. Lavenda, B. H., and Figueiredo, W. (1989).International Journal of Theoretical Physics,28, 391.Google Scholar
  12. Lord Rayleigh (1905).Nature,72, 243.Google Scholar
  13. Mandelbrot, B. (1962).Annals of Mathematical Statistics,33, 1021.Google Scholar
  14. Planck, M. (1899). Über irreversible Strahlungsvorgänge. Fünfte Mitteilung,Berliner Berichte, 440.Google Scholar
  15. Planck, M. (1900).Verhandlung der Deutsches Physikalische Gesellschaft,2, 237.Google Scholar
  16. Planck, M. (1932).Theory of Heat, Macmillan, London, p. 268.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • B. H. Lavenda
    • 1
  1. 1.Università degli StudiCamerinoItaly

Personalised recommendations