A Direct Link between Rényi–Tsallis Entropy and Hölder’s Inequality—Yet Another Proof of Rényi–Tsallis Entropy Maximization

Autor:	Hisa-Aki Tanaka, Masaki Nakagawa, Yasutada Oohama
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Rényi–Tsallis entropy generalized entropy optimization Hölder’s inequality Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 21, Iss 6, p 549 (2019)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e21060549
Popis:	The well-known Hölder’s inequality has been recently utilized as an essential tool for solving several optimization problems. However, such an essential role of Hölder’s inequality does not seem to have been reported in the context of generalized entropy, including Rényi−Tsallis entropy. Here, we identify a direct link between Rényi−Tsallis entropy and Hölder’s inequality. Specifically, we demonstrate yet another elegant proof of the Rényi−Tsallis entropy maximization problem. Especially for the Tsallis entropy maximization problem, only with the equality condition of Hölder’s inequality is the q-Gaussian distribution uniquely specified and also proved to be optimal.
Databáze:	Directory of Open Access Journals
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