Relative Entropies and Jensen Divergences in the Classical Limit

Figure 4

(a) The normalized Kullback Divergence is plotted versus . (b) Normalized generalized relative entropy versus for . As noted in [18], (i) the maximal distance (pseudodistance) between the pertinent PDFs is encountered for , corresponding to the purely quantal situation and (ii) that distance (pseudodistance) grows smaller as augments, tending to vanish for . For the Kullback Divergence description, the size of the transition region looks overestimated if one considers the location of . In (b), the transition region almost disappears.

(a)

(b)