Localization estimation and global vs. local information measures

The maximum entropy principle is one of the great ideas of the last 50 years, with a multitude of applications in many areas of science. Its main ingredient is an information measure. We show that global and local information measures provide different types of physical information, which requires handling them with some care. The concomitant differences are illustrated with reference to the problem of localization in phase space, placing emphasis on some details of the smoothing of Wigner functions, as described in [G. Manfredi, M.R. Feix, Phys. Rev. E 62 (2000) 4665]. Our discussion is made in terms of a special version of Fisher's information measure, called the shift-invariant one.