Conformal Fisher information metric with torsion

Abstract

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. We also briefly comment on the one dimensional classical Ising model and show that the torsion scalar diverges exponentially near criticality.