  This paper focus on investigating the explicit rate of convergence for the
propagation of chaos, in a pathwise sense a family of interacting stochastic
particle related to some Brownian driven McKean-Vlasov dynamics. Precisely the
McKean form of nonlinearity is concentrated on a path dependent drift component
and satisfies a particular sub-gaussian moment control. Such control enables to
derive a uniform estimate of the cost in terms of exponential martingale
between the particle and its McKean/mean-field limit system which in turn
provide an optimal rate of propagation of chaos in terms of the total variation
distance. As a by-product, we deepen some recent propagation of chaos results
due to Lacker 2018 and provides a partial stochastic interpretation of the
entropy control technique introduced in Jabin and Wang 2016.
