  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.
