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.

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