Speaker
Description
Information geometry (IG) 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 (STG). By requiring both curvature and torsion to vanish globally on the statistical manifold, the fundamental properties of the information space can be entirely encoded into the non-metricity tensor. This reframing of IG enable us to distinguish the general $\xi$-parameterized curved space from the $\theta$- (or $\eta$-) parameterized flat space, mirroring the relationship between conventional general relativity and STG. Explicitly, the $\theta$- or $\eta$-coordinates emerge as the special coordinates in the coincident gauge, where all connection coefficients vanish.
This research not only provides a new geometric foundation for IG but also establishes a robust link between “information dissipation” and “the representation of gravity via non-metricity in STG.”