2018/05/13 by Manh Hong Duong, M. H. Duong, Grigorios A. Pavliotis +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #math-ph #math.AP #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.1805.04959
28 pages. Comments are welcome
openalex publication_date 2018/05/13 · openalex created_date 2018/05/17 · arxiv created 2018/05/25 · arxiv updated 2018/05/28 · openalex updated_date 2026/07/28
In this paper, we study the mean field limit of interacting particles with memory that are governed by a system of interacting non-Markovian Langevin equations. Under the assumption of quasi-Markovianity (i.e. that the memory in the system can be described using a finite number of auxiliary processes), we pass to the mean field limit to obtain the corresponding McKean-Vlasov equation in an extended phase space. We obtain the fundamental solution (Green's function) for this equation, for the case of a quadratic confining potential and a quadratic (Curie-Weiss) interaction. Furthermore, for nonconvex confining potentials we characterize the stationary state(s) of the McKean-Vlasov equation, and we show that the bifurcation diagram of the stationary problem is independent of the memory in the system. In addition, we show that the McKean-Vlasov equation for the non-Markovian dynamics can be written in the GENERIC formalism and we study convergence to equilibrium and the Markovian asymptotic limit.