Kullback–Leibler and relative Fisher information as descriptors of locality

Kullback–Leibler and relative Fisher information functionals are applied in studying deviation from
local density approximation. The reduced density gradient s and the local kinetic energy parameter
a are key ingredients of these new locality descriptors. The relative Kullback–Leibler information
density contains extra knowledge as it is negative where the given probability density is smaller
than the reference density. The relative Fisher information incorporates the highest order deviations
from the uniform electron gas approximation.