Axioms and uniqueness theorem for Tsallis entropy

By S. Abe. 2000

168 citations recorded by the source corpus.

Abstract The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy and a complete proof of the uniqueness theorem for the Tsallis entropy is presented. This improves the discussion of dos Santos [J. Math Phys. 38 (1997) 4104].

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/66837d612d095c9fe1564bcf604369beb1ae2c85

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Citations in the corpus

Generalised information and entropy measures in physics (2009, background): “Abe [32] has shown that the Tsallis entropy follows uniquely (up to an arbitrary multiplicative constant) from the following generalised version of the Khinchin axioms.”
State of the field: Measuring information and confirmation (2014, background): “On the background of a few plausible and shared assumptions, entR and entD can be distinctively characterized by their respective additive behavior (see Abe, 2000).”
On non-Gaussianity and dependence in financial time series: a nonextensive approach (2005, background): “Despite the fact that other forms had already been introduced at that time, and still others were presented later, Sq is the only one that respects important properties like concavity and experimental robustness just as Shannon’s does (Abe and Okamoto 2001, Gell-Mann and Tsallis 2004) and last but n”
Principles of maximum entropy and maximum caliber in statistical physics (2013, unknown): “Nonextensive systems were studied in detail, particularly by Tsallis (see also Landsberg, 1972, 1984; Tsallis, 1988; Abe, 2000, 2001; Tsallis, Abe, and Okamoto, 2001; and Tsallis, Gell-Mann, and Sato, 2005).”
Information theoretical properties of Tsallis entropies (2004, methodology): “…used [10, 11], and then important and meaningful results in physics are derived for the normalized nonadditive conditional entropy deﬁned in [6, 10]. x p ( x ) q However, as pointed out in [13], the normalized Tsallis entropies are not stable, but the original Tsallis entropies are stable…”