Phase coexistence beyond onset

As stated in Section H.A, the moment free energy does not give exact results beyond the onset of phase coexistence—that is, in the regime where the coexisting phases occupy comparable fractions of the total system volume. As shown in Section III.A, the calculated phases will still be in exact thermal equilibrium but the lever rule will now be violated for the transverse degrees of freedom of the density distributions. This is clear from Eq. (11) In general, no linear combination of distributions from this family can match the parent p (a) exactly. 

---