  In the mean-field regime, the evolution of a gas of $N$ interacting particles
is governed in first approximation by a Vlasov type equation with a
self-induced force field. This equation is conservative and describes return to
equilibrium only in the very weak sense of Landau damping. However, the first
correction to this approximation is given by the Lenard-Balescu operator, which
dissipates entropy on the very long timescale $O(N)$. In this paper, we show
how one can derive rigorously this correction on intermediate timescales (of
order $O(N^r)$ for $r<1$), close to equilibrium.
