# Deformed Tsallis-statistics analysis of a complex nonlinear matter-field system

## TL;DR

This paper investigates complex dynamics in a classical-quantum system using deformed Tsallis statistics, revealing rich behaviors like chaos and periodicity, and compares these with traditional Shannon-based measures.

## Contribution

It introduces a novel application of deformed Tsallis statistics to analyze the intricate dynamics of a classical-quantum system, highlighting differences from Shannon-based analysis.

## Key findings

- Chaotic and complex behaviors are identified near quantum instability points.
- Tsallis quantifiers provide a different perspective compared to Shannon entropy.
- Rich dynamical regimes include periodic, quasi-periodic, and unbounded behaviors.

## Abstract

We study, using information quantifiers, the dynamics generated by a special Hamiltonian that gives a detailed account of the interaction between a classical and a quantum system. The associated, very rich dynamics displays periodicity, quasi-periodicity, not-boundedness, and chaotic regimes. Chaoticity, together with complex behavior, emerge in the proximity of an unstable entirely quantum instance. Our goal is to compare the statistical description provided by Tsallis quantifiers vis a vis that obtained with Shannon's entropy and Jensen's complexity.