Nonextensive Statistical Mechanics, Anomalous Diffusion and Central Limit Theorems
نویسندگان
چکیده
منابع مشابه
Nonextensive statistical mechanics and central limit theorems I - Convolution of independent random variables and q-product
In this article we review the standard versions of the Central and of the Lévy-Gnedenko Limit Theorems, and illustrate their application to the convolution of independent random variables associated with the distribution Gq (X) ≡ Aq [ 1 +(q−1)Bq (X − μ̄q) ] 1 1−q (Aq > 0; Bq > 0; q < 3), known as q-Gaussian. This distribution emerges upon extremisation of the nonadditive entropy Sq ≡ k (1− ∫ [p(...
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As well known, the standard central limit theorem plays a fundamental role in BoltzmannGibbs (BG) statistical mechanics. This important physical theory has been generalized by one of us (CT) in 1988 by using the entropy Sq = 1− ∑ i p i q−1 (with q ∈ R) instead of its particular case S1 = SBG = − ∑ i pi ln pi. The theory which emerges is usually referred to as nonextensive statistical mechanics ...
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ژورنال
عنوان ژورنال: Milan Journal of Mathematics
سال: 2005
ISSN: 1424-9286,1424-9294
DOI: 10.1007/s00032-005-0041-1