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Truth, belief and experience — a route to information

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Abstract

In gratitude to Klaus Krickeberg who introduced the author to Shannons information theory, this contribution is devoted to certain basic considerations which are consistent with, yet carry you beyond Shannons original ideas from 1948, cf. [13]. Fact is that since Shannons pioneering work — to a great extent centred around the notion of entropy — a jungle of alternative entropy measures have been suggested. Philosophical speculation will lead us through this jungle and lay out a narrow path of special entropy measures, the so-called Tsallis entropies, thereby providing these entropy measures with special credibility.

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References

  1. J. Aczél and Z. Daróczy. On measures of information and their characterizations (Academic Press, New York, 1975).

    MATH  Google Scholar 

  2. R. Ahlswede. “Identification Entropy”. In Ahlswede et al, editor, General Theory of Information Transfer and Combinatorics, Lecture Notes in Computer Science 4123 595–613, Springer, Berlin (2006).

    Chapter  Google Scholar 

  3. P. Sahoo B. Ebanks and W. Sander. Characterizations of Information Measures (World Scientific, Singapore, 1998).

    Google Scholar 

  4. T. Cover and J. A. Thomas. Elements of Information Theory (Wiley, 1991).

  5. Z. Daróczy. Generalized Information Functions. Information and Control 16 36–51 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Havrda and F. Charvát. Quantification method of classification processes. Concept of structural a-entropy. Kybernetika 3 30–35 (1967). Review by I. Csiszár in MR 34 (8875).

    MATH  MathSciNet  Google Scholar 

  7. E. T. Jaynes. Information theory and statistical mechanics, I and II. Physical Reviews 106 and 108 620–630 and 171–190 (1957).

    Article  MathSciNet  Google Scholar 

  8. E. T. Jaynes. Where do we Stand on Maximum Entropy? In R.D. Levine and M. Tribus, editors, The Maximum Entrropy Formalism, 1–104, M.I.T. Press, Cambridge, MA (1979).

    Google Scholar 

  9. D. F. Kerridge. Inaccuracy and inference. J. Roy. Stat. Soc. B. 23 184–194 (1961).

    MATH  MathSciNet  Google Scholar 

  10. J. Lindhard. On the Theory of Measurement and its Consequences in Statistical Dynamics. Mat. Fys. Medd. Dan. Vid. Selsk. 39(1), 1–39 (1974).

    MathSciNet  Google Scholar 

  11. J. Lindhard and V. Nielsen. Studies in Statistical Dynamics. Mat. Fys.Medd. Dan. Vid. Selsk. 38(9), 1–42 (1971).

    Google Scholar 

  12. J. Naudts. Generalised exponential families and associated entropy functions. Entropy 10 131–149 (2008).

    Article  MathSciNet  Google Scholar 

  13. C. E. Shannon. A mathematical theory of communication. Bell Syst. Tech. J. 27 379–423 and 623–656 (1948).

    MATH  MathSciNet  Google Scholar 

  14. F. Topsøe. Exponential Families and MaxEnt Calculations for Entropy Measures of Statistical Physics. In Qurati et al, editors, Complexity, Metastability, and Non-Extensivity, CTNEXT07 AIP Conference Proceedings 965 104–113 (2007).

  15. C. Tsallis. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Physics 52 479–487 (1988). See http://tsallis.cat.cbpf.br/biblio.htm for a comprehensive and updated bibliography.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to F. Topsøe.

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Dedicated to the 80th birthday of Klaus Krickeberg

Original Russian Text © F. Topsøe, 2009, published in Izvestiya NAN Armenii. Matematika, 2009, No. 2, pp. 47–55.

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Topsøe, F. Truth, belief and experience — a route to information. J. Contemp. Mathemat. Anal. 44, 105–110 (2009). https://doi.org/10.3103/S1068362309020046

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