  The propagation of gradient flow structures from microscopic to macroscopic
models is a topic of high current interest. In this paper we discuss this
propagation in a model for the diffusion of particles interacting via hard-core
exclusion or short-range repulsive potentials. We formulate the microscopic
model as a high-dimensional gradient flow in the Wasserstein metric for an
appropriate free-energy functional. Then we use the JKO approach to identify
the asymptotics of the metric and the free-energy functional beyond the lowest
order for single particle densities in the limit of small particle volumes by
matched asymptotic expansions. While we use a propagation of chaos assumption
at far distances, we consider correlations at small distance in the expansion.
In this way we obtain a clear picture of the emergence of a macroscopic
gradient structure incorporating corrections in the free energy functional due
to the volume exclusion.
