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.