  We consider extended slow-fast systems of N interacting diffusions. The
typical behavior of the empirical density is described by a nonlinear
McKean-Vlasov equation depending on , the scaling parameter separating the time
scale of the slow variable from the time scale of the fast variable. Its
atypical behavior is encapsulated in a large N Large Deviation Principle (LDP)
with a rate functional. We study the $\Gamma$-convergence of as $\rightarrow$ 0
and show it converges to the rate functional appearing in the Macroscopic
Fluctuations Theory (MFT) for diffusive systems.
