  We introduce a new approach to justify mean-field limits for first-and
second-order particle systems with singular interactions. It is based on a
duality approach combined with the analysis of linearized dual correlations,
and it allows to cover for the first time arbitrary square-integrable
interaction forces at possibly vanishing temperature. In case of first-order
systems, it allows to recover in particular the mean-field limit to the 2d
Euler and Navier-Stokes equations. We postpone to a forthcoming work the
development of quantitative estimates and the extension to more singular
interactions.
