Speaker
Description
We present information geometry from the perspective of divergences, which define a generally asymmetric notion of separation. From this starting point, we show how both the metric tensor and affine connection naturally emerge, and we emphasize the role of nonmetricity in this framework. Within this setting, we demonstrate that a Brownian bridge subject to a canonical physical constraint evolves exactly along an m-geodesic on the statistical manifold of Gaussian distributions. This provides an explicit example in which stochastic dynamics follows an informationally straight trajectory, in analogy with geodesic motion in general relativity. More broadly, our findings suggest that the asymmetry of divergence may carry genuine physical significance and may constitute a concrete step toward an equivalence principle for information.