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2004•Unpublished venueRequires access

Shannon Entropy, Renyi Entropy, and Information

Paul A. Bromiley, E. V. Bouhova-Thacker

Open publisher page 95 citations

Abstract

This memo contains proofs that the Shannon entropy is the limiting case of both the Renyi entropy and the Tsallis entropy, or information. These results are also confirmed experimentally. We conclude with some general observations on the utility of entropy measures. A brief summary of the origins of the concept of physical entropy are provided in an appendix.

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What this paper is about

This memo contains proofs that the Shannon entropy is the limiting case of both the Renyi entropy and the Tsallis entropy, or information. These results are also confirmed experimentally. We conclude with some general observations on the utility of entropy measures. A brief summary of the origins of the concept of physical entropy are provided in an appendix.

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OpenAlex reports 95 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This memo contains proofs that the Shannon entropy is the limiting case of both the Renyi entropy and the Tsallis entropy, or information. These results are also confirmed experimentally. We conclude with some general observations on the utility of entropy measures. A brief summary of the origins of the concept of physical entropy are provided in an appendix.

Key concepts: Rényi entropy, Min entropy, Mathematics, Tsallis entropy, Joint quantum entropy, Entropy in thermodynamics and information theory, Maximum entropy thermodynamics, Entropy (arrow of time)

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