2007/03/11 by E. Akturk, Akturk, E., G. B. Bagci +3 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0703277
9 pages
arxiv created 2007/03/11 · openalex publication_date 2007/03/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.