Density functional formalism in the canonical ensemble

Density functional theory (DFT), when applied to systems with T not equal 0 , is based on the grand canonical extension of the Hohenberg-Kohn-Sham theo rem due to Mermin (HKSM theorem). While a straightforward canonical ensembl e (CE) generalization fails, work in nanopore systems could certainly benef it from a mesoscopic DFT in the CE. We show that, if the asymptotic behavio ur of the canonical distribution functions is taken into account, the HKSM theorem can be extended to the CE. We generate N-modified correlation and d istribution functions hierarchies, show that their functional relationship is equivalent to the one holding between the more conventional ones and pro ve that, if they are employed, either a modified external field or the dens ity profiles can be indistinctly used as independent variables. We also wri te down the N-modified free energy functional and prove that its minimum is reached when the equilibrium values of the new hierarchy are used. This co mpletes the extension of the HKSM theorem.