Entropy and Its Discontents: A Note on Definitions

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