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arXiv · 2503.09328

Schr\"odinger Bridges for Systems of Interacting Particles

Henri Orland
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Abstract

A Schr\"odinger bridge is the most probable time-dependent probability distribution that connects an initial probability distribution $w_{i}$ to a final one $w_{f}$. The problem has been solved and widely used for the case of simple Brownian evolution (non-interacting particles). It is related to the problem of entropy-regularized Wasserstein optimal transport. In this article, we generalize Brownian bridges to systems of interacting particles. We derive some equations for the forward and backward single particle ``wave-functions'' which allow to compute the most probable evolution of the single-particle probability between the initial and final distributions.

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Henri Orland. 2025-03-12. Schr\"odinger Bridges for Systems of Interacting Particles. https://arxiv.org/abs/2503.09328

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