A criterion for proving entropy chaos on path space
Abstract
A criterion for proving a strong form of propagation of chaos on the path space, known as entropy chaos, for a general interacting diffusion system is proposed. Our analysis focuses on the class of conservative diffusions introduced by Carlen, which are characterized by infinitesimal characteristic pairs, that is, a time-marginal probability density and a current velocity field. A key property of this broad class is that the processes remain diffusions under time-reversal. We prove that, given a suitable bound on the relative entropy (with respect to the Wiener measure) and the weak convergence of both drifts and fixed-time marginal densities, strong entropy chaos at the process level is achieved in the infinite particle limit, provided the limit drift satisfies a specific regularity condition. This stochastic framework encompasses various singular interacting particle systems and their related asymptotic scenarios.
Cite
@article{arxiv.2604.14427,
title = {A criterion for proving entropy chaos on path space},
author = {Luigi Borasi and Francesco Carlo De Vecchi and Stefania Ugolini},
journal= {arXiv preprint arXiv:2604.14427},
year = {2026}
}