On the instability of two entropic dynamical models

TL;DR

This paper investigates the geometric properties and instability characteristics of two entropic dynamical models using information geometry, analyzing their geodesics and Jacobi fields to extend previous research.

Contribution

It provides a detailed geometric analysis of the models' instability by deriving their geodesics and Jacobi fields, extending prior work in the field.

Findings

Identification of instability regions through Jacobi fields

Geometric characterization of the models' dynamics

Extension of previous theoretical results

Abstract

In this paper we study two entropic dynamical models from the viewpoint of information geometry. We study the geometry structures of the associated statistical manifolds. In order to analyse the character of the instability of the systems, we obtain their geodesics and compute their Jacobi vector fields. The results of this work improve and extend a recent advance in this topics studied in [13]