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. 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 case and the θ- or η-parameterized cases, which correspond to general symmetric teleparallel gravity and its coincident gauge, respectively. Specifically, the θ- or η-coordinates emerge as special coordinates in the coincident gauge, where the connection coefficients vanish.
Related
- Foldy--Wouthuysen Transformation of the Generalized Dirac Equation in Symmetric Teleparallel Gravity
- From Nonmetricity Operators to the Physical Spectrum: A Branch-Complete Analysis of Local Four-Derivative Symmetric Teleparallel Gravity
- Testing Extended Exponential Infrared Teleparallel Gravity with CMB, DESI, and PantheonPlus
- Gauge-invariant non-universal scalar couplings in teleparallel gravity
- A new parametric study of f(T) teleparallel gravity with generalized Chaplygin gas: Confronting observational data
BibTeX
@misc{wada2026reframing,
title = {{Reframing of Information Geometry via Symmetric Teleparallel Gravity}},
author = {Tatsuaki Wada},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.00649},
eprint = {2607.00649},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.00649},
}
RIS
TY - UNPB
TI - Reframing of Information Geometry via Symmetric Teleparallel Gravity
AU - Tatsuaki Wada
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2607.00649
UR - https://arxiv.org/abs/2607.00649
AB - 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 case and the θ- or η-parameterized cases, which correspond to general symmetric teleparallel gravity and its coincident gauge, respectively. Specifically, the θ- or η-coordinates emerge as special coordinates in the coincident gauge, where the connection coefficients vanish.
ER -