AI 中文总结
本文利用对称平行重力的几何框架，通过要求统计流形上曲率和挠率全局为零，将信息几何的基本性质编码到非度量张量中，并区分了ξ参数化空间与θ（或η）参数化空间。
AI 中文摘要
信息几何传统上是在黎曼几何和对偶仿射连接的框架内表述的。在这项工作中，我们通过引入对称平行重力的几何机制来重构这一基础结构。通过要求统计流形上的曲率和挠率全局为零，我们证明了信息空间的基本性质可以完全编码到非度量张量中。这种方法使我们能够区分一般的ξ参数化空间与θ（或η）参数化空间，反映了传统广义相对论与对称平行重力之间的关系。具体而言，θ或η坐标作为重合规范中的特殊坐标出现，其中连接系数为零。
英文摘要
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.
Comments14 pages, some explanations are improved
