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Is Sharma-Mittal entropy really a step beyond Tsallis and Renyi entropies? | | E. Akturk
; G. B. Bagci
; R. Sever
; | | Date: |
12 Mar 2007 | | Subject: | Statistical Mechanics | | 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 R’{e}nyi 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 R’{e}nyi entropies but rather only as a generalization of R’{e}nyi 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. | | Source: | arXiv, cond-mat/0703277 | | Services: | Forum | Review | PDF | Favorites | |
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