Information Geometry of Hydrodynamics with Global Anomalies

TL;DR

This paper develops an information geometric framework for hydrodynamics with global anomalies, revealing how system transitions relate to anomaly coefficients through curvature analysis.

Contribution

It introduces a metric on the parameter space of anomalous hydrodynamics and links curvature divergences to universal transition points.

Findings

Curvature on the statistical manifold is affected by system rotations.

Divergences in curvature indicate phase transition points.

Transition points are universally expressed via anomaly coefficient ratios.

Abstract

We construct information geometry for hydrodynamics with global gauge and gravitational anomalies in $1+1$ and $3+1$ dimensions. We introduce the metric on a parameter space and show that turning on non-zero rotations leads to a curvature on the statistical manifold. We calculate the curvature invariant and analyze its divergences, which occur at the transition points of the system. The transition points are universal and expressed in terms of ratios of anomaly coefficients.