A six-dimensional distribution function F is constructed from the one-matrix of a non-interacting system. For double occupied orbitals and real one-matrix, the Fisher information I-F constructed from the distribution function F is proportional to the non-interacting kinetic energy T-s. A local six-dimensional wave-vector q is defined that establishes a link between the Shannon and Fisher information and the local kinetic energy. Illustrative examples for Coulomb systems are presented. (C) 2014 Elsevier B.V. All rights reserved.