In contribution (2.1.13), Helgaker states that he prefers the Legendre-transform formulation. However, it has been shown that the Legendre-transform formulation is equivalent to the ensemble constrained search. (2.1.15) Helgaker : It is of course correct that the ensemble constrained-search functional is identical to Lieb's functional. With respect to the different formulations of DFT, my view is the following.