Finite Temperature Scaling in Density Functional Theory
  A previous analysis of scaling, bounds, and inequalities for the non-interacting functionals of thermal density functional theory is extended to the full interacting functionals. The results are obtained from analysis of the related functionals from the equilibrium statistical mechanics of thermodynamics for an inhomogeneous system. Their extension to the functionals of density functional theory is described. 
James W. Dufty and S.B. Trickey
cond-mat.stat-mech