Entropy 2004, 6[4], 364-374
Entropy
ISSN 1099-4300
http://www.mdpi.org/entropy/

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

Takuya Yamano

Department of Physics, Ochanomizu University,
2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan.
E-mail: [email protected]

Received: 1 June 2004 / Accepted: 31 July 2004 / Published: 1 August 2004

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.


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