2026/07/01 by Tatsuaki Wada
#gr-qc
Information geometry has traditionally been formulated within the framework of Riemannian geometry and dual affine connections. This work aims to reframe the foundational structure of information geometry by introducing the geometric machinery of symmetric teleparallel gravity. By requiring both curvature and torsion to vanish globally on the statistical manifold, it is demonstrated that the fundamental properties of the information space can be entirely encoded in the non-metricity tensor. This approach clarifies the distinction between the general ξ-parameterized space and the θ- (or η-) parameterized space, mirroring the relationship among conventional general relativity, symmetric teleparallel gravity and the coincident gauge in symmetric teleparallel gravity. Specifically, the θ- or η-coordinates emerge as the special coordinates in the coincident gauge, where the connection coefficients vanish.