  We revisit the grazing collision limit connecting the Boltzmann equation to
the Landau(-Fokker-Planck) equation from their recent reinterpretations as
gradient flows. Our results are in the same spirit as the $\Gamma$-convergence
of gradient flows technique introduced by Sandier and Serfaty. In this setting,
the grazing collision limit reduces to showing the lower semi-continuous
convergence of the Boltzmann entropy-dissipation to the Landau
entropy-dissipation.
