Analysis of Tsallis' classical partition function's poles

When one integrates the q-exponential function of Tsallis' so as to get the partition function Z, a gamma function inevitably emerges. Consequently, poles arise. We investigate here the thermodynamic significance of these poles in the case of n classical harmonic oscillators (HO). Given that this is an exceedingly well known system, any new feature that may arise can safely be attributed to the poles' effect. We appeal to the mathematical tools used in Plastino et al. (2016) and Plastino and Rocca (2017), and obtain both bound and unbound states. In the first case, we are then faced with a classical Einstein crystal. We also detect what might be interpreted as pseudo gravitational effects.