On \(q\)-non-extensive statistics with non-Tsallisian entropy. (English) Zbl 1400.94088
Summary: We combine an axiomatics of Rényi with the \(q\)-deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the entropy thus obtained is uniquely solved in terms of a one-parameter family of information measures. The ensuing maximal-entropy distribution is phrased in terms of a special function known as the Lambert W-function. We analyze the corresponding “high” and “low-temperature” asymptotics and reveal a non-trivial structure of the parameter space. Salient issues such as concavity and Schur concavity of the new entropy are also discussed.
MSC:
| 94A15 | Information theory (general) |
| 94A17 | Measures of information, entropy |
| 82B05 | Classical equilibrium statistical mechanics (general) |
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