  We show that there exists a very natural, superstatistics-linked extension of
the central limit theorem (CLT) to deformed exponentials (also called
q-Gaussians): This generalization favorably compares with the one provided by
S. Umarov and C. Tsallis [arXiv:cond-mat/0703533], since the latter requires a
special "q-independence" condition on the data. On the contrary, our CLT
proposal applies exactly in the usual conditions in which the classical CLT is
used. Moreover, we show that, asymptotically, the q-independence condition is
naturally induced by our version of the CLT.

Statistical Mechanics