A note on bounded entropies

Pierre-Olivier Amblard and Christophe Vignat

Physica A: Statistical Mechanics and its Applications, 2006, vol. 365, issue 1, 50-56

Abstract: The aim of the paper is to study the link between non-additivity of some entropies and their boundedness. We propose an axiomatic construction of the entropy relying on the fact that entropy belongs to a group isomorphic to the usual additive group. This allows to show that the entropies that are additive with respect to the addition of the group for independent random variables are nonlinear transforms of the Rényi entropies, including the particular case of the Shannon entropy. As a particular example, we study as a group a bounded interval in which the addition is a generalization of the addition of velocities in special relativity. We show that Tsallis–Havrda–Charvat entropy is included in the family of entropies we define. Finally, a link is made between the approach developed in the paper and the theory of deformed logarithms.

Keywords: Non-additivity; Bounded groups; Lorentz law; Tsallis–Havrda–Charvat entropy (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:365:y:2006:i:1:p:50-56

DOI: 10.1016/j.physa.2006.01.002

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