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Is Sharma-Mittal entropy really a step beyond Tsallis and Renyi entropies?

E. Akturk·G. B. Bagci·R. Sever
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Abstract

We studied the Sharma-Mittal relative entropy and showed that its physical meaning is the free energy difference between the off-equilibrium and equilibrium distributions. Unfortunately, Sharma-Mittal relative entropy may acquire this physical interpretation only in the limiting case when both parameters approach to 1 in which case it approaches Kullback-Leibler entropy. We also note that this is exactly how Rényi relative entropy behaves in the thermostatistical framework thereby suggesting that Sharma-Mittal entropy must be thought to be a step beyond not both Tsallis and Rényi entropies but rather only as a generalization of Rényi entropy from a thermostatistical point of view. Lastly, we note that neither of them conforms to the Shore-Johnson theorem which is satisfied by Kullback-Leibler entropy and one of the Tsallis relative entropies.

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E. Akturk, G. B. Bagci, R. Sever. 2007-03-11. Is Sharma-Mittal entropy really a step beyond Tsallis and Renyi entropies?. https://arxiv.org/abs/cond-mat/0703277

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