The Gravitational Aspect of Information: The Physical Reality of Asymmetric "Distance"

TL;DR

This paper demonstrates that constrained Brownian bridges follow geodesics in the space of Gaussian distributions, linking information geometry with physical processes and highlighting the fundamental role of asymmetrical informational distance.

Contribution

It establishes a physical realization of geodesics in information geometry through constrained Brownian bridges, connecting geometric and physical concepts.

Findings

Brownian bridges under constraints follow m-geodesics

Information divergence asymmetry has a fundamental physical role

Provides a geometric interpretation of physical processes in information space

Abstract

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.