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

Entropy and Its Discontents: A Note on Definitions

Dipartimento di Matematica and TIRES, Universit脿 di Bari, INFN Sezione di Bari via E. Orabona 4, 70125 Bari, Italy
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 (CC BY 3.0).

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

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