On a \(q\) -central limit theorem consistent with nonextensive statistical mechanics
The basic operations of the \(q\)-algebra are defined as \(x\oplus_q y=x+y+(1-q)xy\) and \(x\otimes_q y=[x^{1-q}+y^{1-q} -1]_+^{\frac{1}{1-q}}.\) The \(q\)-generalization of the classic entropy introduced in [\textit{C. Tsallis}, J. Stat. Phys. 52, No.~1--2, 479--487 (1988; Zbl 1082.82501)] given by \(S_q=\frac{1-\sum_i p_i^q}{q-1}\),with \(q\in R\) and \(S_1=S_{BG}\), reaches its maximum at the distributions named \(q\)-Gaussians. The authors prove a generalization of Central Limit Theorem for \(1\leq q<3\).
\(q\)-generalization of the classic entropy
scientific article; zbMATH DE number 5624129
scientific article