Statistical permutation quantifiers in the classical transition of conservative-dissipative systems

TL;DR

This paper investigates the behavior of a nonlinear semiclassical system in conservative and dissipative regimes using Shannon entropy and statistical complexity, revealing three distinct dynamical regions.

Contribution

It introduces a novel analysis combining permutation-based probability distributions with information metrics to study semiclassical systems.

Findings

Identification of three distinct dynamical regions including a mesoscopic one

Application of permutation entropy and complexity to semiclassical systems

Insights into classical limit via a motion invariant related to the uncertainty principle

Abstract

We study the behavior of a nonlinear semiclassical system using Shannon entropy and two approaches to statistical complexity. These systems involve the interaction between classical variables (representing the environment) and quantum ones. Both conservative and dissipative regimes are explored. To calculate the information metrics, probability distributions are derived from the temporal evolution via the Bandt-Pompe permutation method. Additionally, we describe the classical limit in terms of a motion invariant linked to the uncertainty principle. Our analysis reveals three distinct regions, including a mesoscopic one, along with other notable findings.