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

Tomoi Koide; Armin van de Venn

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arXiv · 2510.22664

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

Tomoi Koide·Armin van de Venn

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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.

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cond-mat.stat-mech cs.IT gr-qc hep-ph math.IT math.ST quant-ph stat.TH

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Tomoi Koide, Armin van de Venn. 2025-10-26. The Gravitational Aspect of Information: The Physical Reality of Asymmetric "Distance". https://arxiv.org/abs/2510.22664

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