  We consider the Gross-Pitaevskii(GP) model of a Bose-Einstein Condensate(BEC)
with non-local s-wave interactions. The non-locality is represented by
corrections to the local GP equation. Due to such corrections to the GP
equation, there arise corrections to the free energy functional as well. We
present here a proof of the exact correspondence between the free energy and
the dynamics for typical terms appearing while considering corrections to the
GP equation at any order. This non-trivial correspondence can be used to study
BECs perturbatively while going beyond the Fermi pseudopotential.
