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.

Entropy and Its Discontents: A Note on Definitions

CUFARO PETRONI, Nicola
2014-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/38119
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