Multi-species McKean-Vlasov dynamics in non-convex landscapes
Abstract
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system, propagation of chaos and the derivation of the coupled McKean-Vlasov PDE system in the mean field limit. Our focus is on the long-time and asymptotic behaviour of the mean-field PDEs. Under suitable growth assumptions on the potentials and an appropriate structural assumption, we show the existence and (non-) uniqueness of stationary solutions and study their linear stability. Under a symmetry assumption we construct a free-energy functional that plays the role of a Lyapunov function for the mean-field PDE system. Furthermore, we prove the existence of a phase transition at low noise strengths and establish the convergence of solutions to the mean-field PDEs (and of their free energy) to a stationary state (and the corresponding free energy).
Keywords
Cite
@article{arxiv.2507.07617,
title = {Multi-species McKean-Vlasov dynamics in non-convex landscapes},
author = {Manh Hong Duong and Grigorios A. Pavliotis and Julian Tugaut},
journal= {arXiv preprint arXiv:2507.07617},
year = {2025}
}