We consider a system of indistinguishable classical particles in Euclidean space interacting through a short-range pair potential. Fixing the one-particle density profile of the system, we minimize the free energy over the set of states with this exact density. This can be useful e.g. to model interfaces between two different equilibrium phases of a system. In this talk, I will discuss how to approximate the free energy in terms of a local functional depending only on the density of the system. The approximation is especially useful when the density is almost constant over large regions of space. This is joint work with Mathieu Lewin and Michal Jex.

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