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：我们证明，当布朗桥被物理约束以满足一个正则条件时，其时间演化与高斯分布统计流形上的 m-测地线精确重合。这一对应为信息几何中的几何概念提供了直接的物理实现。它意味着纯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。我们的发现表明，信息“距离”（散度）的非对称性起着根本的物理作用，为信息的等效原理提供了具体的一步。