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2 results

  • 4 - Deformations of Shannon Entropy

  • Tom Leinster, University of Edinburgh
  • Book:
    Entropy and Diversity
    Published online:
    21 April 2021
    Print publication:
    22 April 2021, pp 91-132

  • Summary

    We introduce two families of deformations of Shannon entropy: the q-logarithmic entropies (also called “Tsallis entropies”) and the Rényi entropies. We explain how the exponentials of the Rényi entropies, called the Hill numbers, convey information about the diversity and structure of an ecological community. We introduce the power means, which lie at the technical heart of this book. We give functional equations characterizing the q-logarithmic entropies on the one hand, and the Hill numbers on the other.