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Correlated Gaussian systems exhibiting additive power-law entropies

C. Vignat·A. Plastino·A. R. Plastino
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Abstract

We show, on purely statistical grounds and without appeal to any physical model, that a power-law $q-$entropy $S_q$, with $0<q<1$, can be {\it extensive}. More specifically, if the components $X_i$ of a vector $X \in \mathbb{R}^N$ are distributed according to a Gaussian probability distribution $f$, the associated entropy $S_q(X)$ exhibits the extensivity property for special types of correlations among the $X_i$. We also characterize this kind of correlation.

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C. Vignat, A. Plastino, A. R. Plastino. 2005-12-20. Correlated Gaussian systems exhibiting additive power-law entropies. https://doi.org/10.1016/j.physleta.2006.01.041

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