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Shannon entropy: axiomatic characterization and application

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  • C. G. Chakrabarti
  • Indranil Chakrabarty

Abstract

We have presented a new axiomatic derivation of Shannon entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function. We have then modified Shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon differential entropy. As an application, we have derived the expression for classical entropy of statistical mechanics from the quantized form of the entropy.

Suggested Citation

  • C. G. Chakrabarti & Indranil Chakrabarty, 2005. "Shannon entropy: axiomatic characterization and application," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:234590
    DOI: 10.1155/IJMMS.2005.2847
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    Cited by:

    1. Zhiyi Zhang, 2020. "Generalized Mutual Information," Stats, MDPI, vol. 3(2), pages 1-8, June.
    2. Jangho Yang, 2018. "Information Theoretic Approaches In Economics," Journal of Economic Surveys, Wiley Blackwell, vol. 32(3), pages 940-960, July.
    3. Mikhail Gennadjevich Goryachev, 2015. "Finite Component Approach for Modelling Entropy of Motor Road Pavements to Assess Their Efficiency," Modern Applied Science, Canadian Center of Science and Education, vol. 9(8), pages 140-140, August.

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