In this paper we study a second-order mean-field stochastic differential
systems describing the movement of a particle under the influence of a
time-dependent force, a friction, a mean-field interaction and a space and
time-dependent stochastic noise. Using techniques from Malliavin calculus, we
establish explicit rates of convergence in the zero-mass limit
(Smoluchowski-Kramers approximation) in the $L^p$-distances and in the total
variation distance for the position process, the velocity process and a
re-scaled velocity process to their corresponding limiting processes.
