We strengthen the connection between information theory and quantum mechanical systems using a recently developed dequantization procedure which results in a decomposition of the kinetic energy as the sum of a classical term and a purely quantum term. For the nearly uniform electron gas, we thereby approximate the noninteracting kinetic energy as the sum of the Thomas-Fermi term, which is exact for the uniform electron gas, and the Weizsäcker term, which is proportional to the Fisher information. Electron correlation is included via a nonlocal analytical expression which is a functional of the (N-1)-conditional probability density. This expression is evaluated via a statistically rigorous Monte-Carlo procedure to obtain the correlation energy as a functional of the electron density. We show that this functional is well aproximated by a term which is proportional to the Shannon entropy. Thus the kinetic energy is expressed as the standard Thomas-Fermi term plus terms which are proportional to two of the cornerstones of information theory: the Fisher information, which is a measure of localization, and the Shannon entropy, which is a measure of delocalization. © 2010 Springer Science+Business Media, LLC.4817882Vedral, V., (2006) Introduction to Quantum Information Science, , Oxford: Oxford University PressFisher, R.A., (1925) Proc. Camb. Philos. Soc., 22, pp. 700-725Nagy, A., (2003) J. Chem. Phys., 119, pp. 9401-9405Romera, E., Dehesa, J.S., (2004) J. Chem. Phys., 120, pp. 8906-8912Sen, K.D., Antolín, J., Angulo, J.C., (2007) Phys. Rev. A, 76, p. 032502. , (7 pages)Parr, R.G., Yang, W., (1989) Density Functional Theory of Atoms and Molecules, , Oxford: Oxford University PressThomas, L.H., (1927) Proc. Cambridge Philos. Soc., 23, pp. 542-548Fermi, E., (1927) Rend. Accad. Lincei, 6, pp. 602-607von Weizsäcker, C.F., (1935) Z. Phys., 96, pp. 431-458Mosna, R.A., Hamilton, I.P., Delle Site, L., (2005) J. Phys. A, 38, pp. 3869-3878Mosna, R.A., Hamilton, I.P., Delle Site, L., (2006) J. Phys. A, 39, pp. L229-L235Hamilton, I.P., Mosna, R.A., Delle Site, L., (2007) Theor. Chem. Acct., 118, pp. 407-415Delle Site, L., (2007) J. Phys. A, 40, pp. 2787-2792Ghiringhelli, L.M., Delle Site, L., (2008) Phys. Rev. B, 77, p. 073104. , (4 pages)