We show that when a Brownian bridge is physically constrained to satisfy a canonical condition, its time evolution exactly coincides with an m-geodesic on the statistical manifold of Gaussian distributions. This identification provides a direct physical realization of a geometric concept in information geometry. It implies that purely random processes evolve along informationally straight trajectories, analogous to geodesics in general relativity. Our findings suggest that the asymmetry of informational ``distance" (divergence) plays a fundamental physical role, offering a concrete step toward an equivalence principle for information.

翻译：本文证明，当布朗桥受物理约束满足正则条件时，其时间演化过程与高斯分布统计流形上的m测地线完全吻合。这一对应关系为信息几何中的几何概念提供了直接的物理实现。这意味着纯粹随机过程沿着信息意义上的直线轨迹演化，类似于广义相对论中的测地线。我们的研究结果表明，信息“距离”（散度）的非对称性发挥着基础性的物理作用，为建立信息的等效原理提供了具体进展。