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Entropy 2014, 16(7), 3732-3753; doi:10.3390/e16073732

On the Connections of Generalized Entropies With Shannon and Kolmogorov–Sinai Entropies

Department of Mathematics, Cracow University of Economics, Rakowicka 27, 31-510 Kraków, Poland
Received: 17 May 2014 / Revised: 19 June 2014 / Accepted: 30 June 2014 / Published: 3 July 2014
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Abstract

We consider the concept of generalized Kolmogorov–Sinai entropy, where instead of the Shannon entropy function, we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this function, we show that this isomorphism invariant is linearly dependent on the Kolmogorov–Sinai entropy.
Keywords: dynamical entropy; Kolmogorov–Sinai entropy dynamical entropy; Kolmogorov–Sinai entropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Falniowski, F. On the Connections of Generalized Entropies With Shannon and Kolmogorov–Sinai Entropies. Entropy 2014, 16, 3732-3753.

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