# Analysis of Tsallis' classical partition function's poles

## TL;DR

This paper explores the mathematical poles in Tsallis' classical partition function for harmonic oscillators and examines their thermodynamic implications, revealing bound states and potential pseudo gravitational effects.

## Contribution

It analyzes the significance of poles in Tsallis' partition function for harmonic oscillators, linking mathematical features to physical phenomena like bound states and pseudo gravity.

## Key findings

- Identification of bound and unbound states due to poles
- Detection of pseudo gravitational effects
- Application of advanced mathematical tools to classical systems

## Abstract

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 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 [EPJB 89, 150 (2016) and arXiv:1702.03535 (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.