  In this paper we consider a system of $N$ particles on the real line evolving
according to Newton's law, interacting through a singular (repulsive) force
deriving from the potential $\frac{|x|^{1-\alpha}}{1-\alpha}$ with $\alpha \in
(0,1/8)$ and Brownian force. Thanks to the entropy dissipation along the
Liouville equation associated to this particles system and a control of the
mechanic energy, we establish a quantitative estimate which enables to conclude
to a convergence/consistency the particles system toward the limiting
Vlasov-Fokker-Planck equation with singular force.
