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It ts known that Tsallis' q-non-additivity entails hidden correlations. Ithas also been shown that even for a monoatomic gas, both the q-partitionfunction $Z$ and the mean energy $<U>$ diverge and, in particular, exhibitpoles for certain values of the Tsallis non additivity parameter $q$. Thishappens because $Z$ and $<U>$ both depend on a $\Gamma$-function. This$\Gamma$, in turn, depends upon the spatial dimension $\nu$. We encounter threedifferent regimes according to the argument $A$ of the $\Gamma$-function. (1)$A>0$, (2) $A<0$ and $\Gamma>0$ outside the poles. (3) $A$ displays poles andthe physics is obtained via dimensional regularization. In cases (2) and (3)one discovers gravitational effects and quartets of particles. Moreover, boundstates and gravitational effects emerge as a consequence of the hiddenq-correlations.

Hidden correlations entailed by q-non additivity render the q-monoatomic gas highly non trivial