Projected free energies for polydisperse phase equilibria

A "polydisperse" system has an infinite number of conserved densities. We give a rational procedure for projecting its infinite-dimensional free energy surface onto a subspace comprising a finite number of linear combinations of densities ("moments"), in which the phase behavior is then found as usual. If the excess free energy of the system depends only on the moments used, exact cloud, shadow, and spinodal curves result; two-phase and multiphase regions are approximate, but refinable indefinitely by adding extra moments. The approach is computationally robust and gives new geometrical insights into the thermodynamics of polydispersity.