Fisher information and density functional theory

Relationship of Fisher information and density functional theory is reviewed. Links between the Fisher and Shannon information, the local wave-vector and the relative information are displayed. Euler equations for the Fisher and relative Fisher information are presented. A combined information theoretical and thermodynamic view of density functional theory is analyzed. The extremum of the Shannon and Fisher information results a constant temperature and for Coulomb systems a simple relation between the total energy and phase-space Fisher information. Relations for phase-spase fidelity, fidelity susceptibility and relative information are also presented.