Bridging between Rényi-Tsallis Entropy and Hölder’s Inequality

Created by: Chigusa Hamada

 Tanaka, Nakagawa and Oohama identify a direct link between Rényi–Tsallis entropy and Hölder’s inequality. Specifically, they 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.

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Chigusa, Hamada. Bridging between Rényi-Tsallis Entropy and Hölder’s Inequality, Encyclopedia, 2019, v1, Available online: https://encyclopedia.pub/202