Reframing of Information Geometry via Symmetric Teleparallel Gravity

Abstract

Information geometry has traditionally been formulated within the framework of Riemannian geometry and dual affine connections. In this work, we reframe this foundational structure by introducing the geometric machinery of symmetric teleparallel gravity. By requiring both curvature and torsion to vanish globally on the statistical manifold, we demonstrate that the fundamental properties of the information space can be entirely encoded into the non-metricity tensor. This approach allows us to distinguish the general $ξ$-parameterized space from the $θ$- (or $η$-) parameterized space, mirroring the relationship between conventional general relativity and symmetric teleparallel gravity. Specifically, the $θ$- or $η$-coordinates emerge as the special coordinates in the coincident gauge, where the connection coefficients vanish.