On the scaling properties of the correlation term of the electron kinetic functional and its relation to the Shannon measure

In a previous work (Ghiringhelli L. M. and Delle Site L., Phys. Rev. B, 77 (2008) 073104) we have proposed a methodological approach to determine the electron correlations contained in the kinetic functional. Its application to the test case of an almost uniform interacting electron gas led to a local density functional of the form integral rho(r)ln rho(r) dr. In this work we discuss the interpretation of such a result by performing an analysis of the formal and numerical properties of the functional under the process of coordinates' scaling. On the basis of such an analysis we propose a local analytic form of the kinetic functional of which the previous numerical result is a first-order approximation. Copyright (C) EPLA, 2009