Entropy, Information and Quantum Geometry

  • Eduardo R. Caianiello
Part of the NATO ASI Series book series (NSSB, volume 135)


This Chinese apophthegm paraphrases here the equivalent one “Entropy is not Shannon Entropy”. There are in fact at least two things wrong with Shannon entropy. The first is its name: had Claude Shannon not accepted John von Neumann’s advice (“you should call it entropy and for two reasons: first, the function is already in use in thermodynamics under that name; second and more importantly, most people don’t know what entropy really is, and if you use the word “entropy in an argument, you will win every time (1)”) and just called it “uncertainty”, endless confusion would have been spared. “Entropy” is psychologically tied with “thermodynamics” in a physicist’s mind, so that the purely logical, far wider connotation of Shannon’s concept escapes attention. Shannon entropy is simply and avowedly the “measure of the uncertainty inherent in a preassigned probability scheme”; as such it has nothing whatever to do with thermodynamica1 entropy, except in the case in which that probability distribution is known, or proven to be, “canonical”.


Shannon Entropy Cross Entropy Quantum Geometry White Horse Abelian Gauge Field 
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  1. 1.
    M. Tribus: “Rational Descriptions decisions and designs”, Pergamon Press,Oxford,1969.Google Scholar
  2. 2.
    E.T. Jaynes: Phys.Revs 106,620 (1952); in “Brandeis Theor. Phys.Lectures on Statistical Physics”Vol. 3(New York)Google Scholar
  3. 3.
    M.Tribus: Journ.Appl.Mech. 28, 1 (1961).MathSciNetGoogle Scholar
  4. 4.
    R.E.Kaiman: “Proc.Int.Symp on Dynamical Systems”,ed.A. Bednarek; “Current Developments in the Interface: Economics, Econometrics, Mathematics”, ed., S.M.Hazenwinkel and A.H. G. Rinnoy Kan (Dordrecht,1982)Google Scholar
  5. 5.
    S.C. Kulback: “Information Theory and Statistics”, J. Wiley, New York,1959.Google Scholar
  6. 6.
    H. Jeffreys: “Theory of Probability” 2nd ed., Clarenton Press,Oxford,1948.zbMATHGoogle Scholar
  7. 7.
    R.A. Fisher: “Phi1.Trans.Roy.Soc. 222A, 309 (1921)” Proc. Cambridge Phil.Soc. 122, 700 (1925).Google Scholar
  8. 8.
    F.Weinhold: Journ.Chem.Phys. 63, 2479/2496 (1975).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    S.Amari: Raag.Reps. 106,Febr.1980; Techn.Reps.Fac.Eng.Univ. of Tokyo,METR 81-1,Aprii 1981;ib,METR 84-1,Jan.1984. B.Efron: Ann.Statist. (1975); 6,362 (1978). A.P.Dawid Ann.Statistic 3, 1231 (1975); 5, 1249 (1977).Google Scholar
  10. 10.
    J.N.Kapur: Journ.Matti.Phys.Sci. 17, 103 (1983).MathSciNetzbMATHGoogle Scholar
  11. 11.
    E.R.Caianiello:Lett.Nuovo Cimento 25,225 (1979); 27,89 (1980); 38,539 (1983); 35,381 (1982);Nuovo Cimento 59B 350 (Ì980); Proc.IV Conf. on Quantum Theory and the Structure of Space and Time,Tutzing (1980); Proc. VI JINR Int. Conf.on Problems of Quantum Theory,Alushta (1980); (with G.Vilasi):Lett.Nuovo Cimento 30,469 (1981); (with G.Vilasi and S.De Filippo) ib, 33,555 (1982); (with G. Marmo and G.Scarpetta), ib, 36,487 (1983); several other papers inprint.Google Scholar
  12. 12.
    E.R.Caianiello: Lett.Nuovo Cimento, 38, 539 (1983).MathSciNetCrossRefGoogle Scholar
  13. 13.
    N.N. Chentzov: “Statistical Decision rules and Optimal Conclusions” (in Russian) Moscow, 1972.Google Scholar
  14. 14.
    C.R.Rao: “Linear statistical Inference and its applications” J. Wiley,New York,1973,and papers quoted therein.zbMATHCrossRefGoogle Scholar
  15. 15.
    R.A. Fisher: cf.Ref.7,b.Google Scholar
  16. 16.
    E.R.Caianiello,G.Marmo,G.Scarpetta: “(Pre) quantum Geometry”, Nuovo Cimento,in print.Google Scholar
  17. 17.
    E.R.Caianiello: Lett.Nuovo Cimento 32,65 (1981);(with S.De Filippo,G.Marmo;G.Vilasi), ib, 34, 112 (1982).MathSciNetCrossRefGoogle Scholar
  18. 18.
    J.A. Wheeler: “Frontiers of Time” LXXII Course Varenna,1977Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Eduardo R. Caianiello
    • 1
  1. 1.Dipartimento Di Fisica Teorica E Sue Metodologie Per Le Scienze ApplicateUniversita’ Di SalernoItaly

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