Propagation of chaos in Fisher information

Jules Grass; Arnaud Guillin; Christophe Poquet

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arXiv · 2511.20078

Propagation of chaos in Fisher information

Jules Grass·Arnaud Guillin·Christophe Poquet

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Abstract

We present a new method for proving sharp local propagation of chaos in Fisher Information for particles with smooth interaction and drift. We rely on a new Lemma computing the Fisher Information of two diffusion processes with smooth drifts and fine estimates on the hessian of the law of the solution of the McKean-Vlasov equation. It allows us to obtain a new propagation of chaos in Fisher information, generalizing Lacker's seminal work by using the BBGKY hierarchy to obtain a system of differential inequalities satisfied by both the relative entropy and the Fisher Information of k particles. We also show with a simple Gaussian example that our decay rate is optimal.

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Jules Grass, Arnaud Guillin, Christophe Poquet. 2025-11-25. Propagation of chaos in Fisher information. https://arxiv.org/abs/2511.20078

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