Extension of Information Geometry to Non-statistical Systems: Some Examples

TL;DR

This paper extends information geometry to non-statistical systems and experimental data, including quantum systems and Bose gases, addressing challenges like the border problem in modeling.

Contribution

It introduces a framework for applying information geometry beyond statistical models, incorporating quantum systems and non-statistical data.

Findings

Extended information geometry to quantum systems with density matrices

Analyzed the border problem in non-statistical models

Applied the framework to Bose gas in grand canonical ensemble

Abstract

Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a statistical manifold. An example of the former is the description of the Bose gas in the grand canonical ensemble. An example of the latter is the modeling of quantum systems with density matrices. Conditional expectations in the quantum context are reviewed. The border problem is discussed: through conditioning the model point shifts to the border of the differentiable manifold.