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Entropy 2004, 6(4), 364-374; doi:10.3390/e6040364

On a simple derivation of a family of nonextensive entropies from information content

Department of Physics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan
Received: 1 June 2004 / Accepted: 31 July 2004 / Published: 1 August 2004
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Abstract

The nonextensive entropy of Tsallis can be seen as a consequence of postulates on a self-information, i.e., the constant ratio of the first derivative of a self-information per unit probability to the curvature (second variation) of it. This constancy holds if we regard the probability distribution as the gradient of a self-information. Considering the form of the nth derivative of a self-information with keeping this constant ratio, we arrive at the general class of nonextensive entropies. Some properties on the series of entropies constructed by this picture are investigated.
Keywords: information theory; nonadditive entropy; information content information theory; nonadditive entropy; information content
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Yamano, T. On a simple derivation of a family of nonextensive entropies from information content. Entropy 2004, 6, 364-374.

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