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Khinchin–Shannon Generalized Inequalities for “Non-additive” Entropy Measures

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Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics

Abstract

Some useful inequalities have been derived by Shannon and rederived by Khinchin which apply to finite probability spaces composed by elementary events. Our fundamental aim here is the study of “non-additive” entropy measures calculated from probabilities of occurrence of amino acids in protein domain families (PDF). These generalized inequalities will provide useful results as the information on the evolution of PDFs is concerned.

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References

  1. A.I. Khinchin, Mathematical Foundations of Information Theory (Dover, New York, 1957)

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  2. G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities (Cambridge University Press, London, 1934)

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  3. B.H. Lavenda, A New Perspective on Thermodynamics (Springer, New York, 2010)

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  4. R.P. Mondaini, S.C. de Albuquerque Neto, The protein family classification in protein databases via entropy measures. ArXiv: 1806.05172 [q-bio.BM] (2018)

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  5. R.P. Mondaini, S.C. de Albuquerque Neto, The pattern recognition of probability distributions of amino acids in protein families, in Mathematical Biology and Biological Physics (World Scientific, Singapore, 2017), pp. 29–50

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Authors and Affiliations

  1. Federal University of Rio de Janeiro, Centre of Technology, COPPE, Rio de Janeiro, RJ, Brazil

    Rubem P. Mondaini & Simão C. de Albuquerque Neto

Authors
  1. Rubem P. Mondaini
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  2. Simão C. de Albuquerque Neto
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Corresponding author

Correspondence to Rubem P. Mondaini .

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Editors and Affiliations

  1. Federal University of Rio de Janeiro, President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Rio de Janeiro, Brazil

    Rubem P. Mondaini

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Mondaini, R.P., de Albuquerque Neto, S.C. (2019). Khinchin–Shannon Generalized Inequalities for “Non-additive” Entropy Measures. In: Mondaini, R. (eds) Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-23433-1_13

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