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Entropy 2014, 16(7), 4044-4059; doi:10.3390/e16074044
Article

Entropy and Its Discontents: A Note on Definitions

Received: 29 May 2014 / Revised: 27 June 2014 / Accepted: 8 July 2014 / Published: 17 July 2014
(This article belongs to the Section Information Theory)
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Abstract

The routine definitions of Shannon entropy for both discrete and continuous probability laws show inconsistencies that make them not reciprocally coherent. We propose a few possible modifications of these quantities so that: (1) they no longer show incongruities; and (2) they go one into the other in a suitable limit as the result of a renormalization. The properties of the new quantities would slightly differ from that of the usual entropies in a few other respects.
Keywords: Shannon entropy; continuous and discrete probability laws; renormalization Shannon entropy; continuous and discrete probability laws; renormalization
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Petroni, N.C. Entropy and Its Discontents: A Note on Definitions. Entropy 2014, 16, 4044-4059.

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