Correlated Gaussian systems exhibiting additive power-law entropies

C. Vignat; A. Plastino; A. R. Plastino

doi:10.1016/j.physleta.2006.01.041

paper

Correlated Gaussian systems exhibiting additive power-law entropies

arXiv:cond-mat/0512511 · doi:10.1016/j.physleta.2006.01.041

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 $X \in R^{N}$ 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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