Propagation of chaos in path spaces via information theory

We study the mean-field limit of the stochastic interacting particle systems via tools from information theory. The key in our method is that, after applying the data processing inequality, one only needs to handle independent copies of solutions to the mean-field McKean stochastic differential equations, which then allows one to apply the law of large numbers. Our result on the propagation of chaos in path space is valid for both first and second order interacting particle systems; in particular, for the latter one our convergence rate is independent of the particle mass and also only linear in time. Our framework is different from current approaches in literature and could provide new insight for the study of interacting particle systems.