Conformal Fisher information metric with torsion

TL;DR

This paper introduces a conformal Fisher information metric with torsion in information geometry, providing a new scalar quantity that distinguishes probability distributions with similar scalar curvature, with applications to thermodynamic models.

Contribution

It defines a torsion-inclusive conformal Fisher information metric for a broad class of systems, extending thermodynamic geometry analysis with a new torsion scalar.

Findings

Torsion scalar exhibits non-trivial behavior on the spinodal curve.

Differentiates probability distributions with identical scalar curvature.

Applied to Van der Waals and Curie-Weiss models.

Abstract

We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate between probability distribution functions that otherwise have the same scalar curvature and hence define similar geometries. In the context of thermodynamic geometry, our construction gives rise to a new scalar - the torsion scalar defined on the manifold, while retaining known physical features related to other scalar quantities. We analyse this in the context of the Van der Waals and the Curie-Weiss models. In both cases, the torsion scalar has non trivial behaviour on the spinodal curve.