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

## TL;DR

This paper explores how Tsallis' q-non-additivity introduces hidden correlations in a q-monoatomic gas, leading to divergences, gravitational effects, and bound states, analyzed through gamma functions and dimensional regularization.

## Contribution

It reveals the complex effects of q-non-additivity on a monoatomic gas, including divergences and emergent phenomena like gravitational effects and bound states, using gamma function analysis.

## Key findings

- Divergences in partition function and mean energy depend on gamma function poles.
- Emergence of gravitational effects and particle bound states due to q-correlations.
- Dimensional regularization resolves physics at gamma function poles.

## Abstract

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.