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

It ts known that Tsallis' q-non-additivity entails hidden correlations. It has also been shown that even for a monoatomic gas, both the q-partition function $Z$ and the mean energy $<U>$ diverge and, in particular, exhibit poles for certain values of the Tsallis non additivity parameter $q$. This happens because $Z$ and $<U>$ both depend on a $\Gamma$-function. This $\Gamma$, in turn, depends upon the spatial dimension $\nu$. We encounter three different 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 and the physics is obtained via dimensional regularization. In cases (2) and (3) one discovers gravitational effects and quartets of particles. Moreover, bound states and gravitational effects emerge as a consequence of the hidden q-correlations.
Comment: Text has changed. Accepted for publication in Physica A, August 2, 2017