We strengthen the connection between information theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization procedure results in a decomposition of the quantum kinetic energy as the sum of a classical term and a purely quantum term. The purely quantum term, which results from the quantum fluctuations, is essentially identical to the Fisher information. The classical term is complementary to the Fisher information and, in this sense, it plays a role analogous to that of the Shannon entropy. We demonstrate the kinetic energy decomposition for both stationary and nonstationary states and employ it to shed light on the nature of kinetic energy functionals.© 2009 Elsevier B.V. All rights reserved.233615421547Dehesa, J.S., Lopez-Rosa, S., Olmos, B., Yanez, R.J., Information measures of hydrogenic systems, Laguerre polynomials and spherical harmonics (2005) Journal of Computational and Applied Mathematics, 179, pp. 185-194. , DOI 10.1016/j.cam.2004.09.040, PII S0377042704004480Dehesa, J.S., Martinez-Finkelshtein, A., Sorokin, V.N., Information-theoretic measures for Morse and Pöschl-Teller potentials (2006) Molecular Physics, 104 (4), pp. 613-622. , DOI 10.1080/00268970500493243, PII K50556650768Dehesa, J.S., González-Férez, R., Sánchez-Moreno, P., The Fisher-information-based uncertainty relation, Cramer-Rao inequality and kinetic energy for the D-dimensional central problem (2007) J. Phys. A, 40, pp. 1845-1856Romera, E., Sanchez-Moreno, P., Dehesa, J.S., The Fisher information of single-particle systems with a central potential (2005) Chemical Physics Letters, 414 (4-6), pp. 468-472. , DOI 10.1016/j.cplett.2005.08.032, PII S0009261405011966Romera, E., Sánchez-Moreno, P., Dehesa, J.S., Uncertainty relation for Fisher information of D-dimensional single-particle systems with central potentials (2006) J. Math. Phys., 47, p. 103504Sánchez-Moreno, P., González-Férez, R., Dehesa, J.S., Improvement of the Heisenberg and Fisher-information-based uncertainty relations for D-dimensional central potentials (2006) New J. Phys., 8, p. 330Mosna, R.A., Hamilton, I.P., Site, L.D., Quantum-classical correspondence via a deformed kinetic operator (2005) Journal of Physics A: Mathematical and General, 38 (17), pp. 3869-3878. , DOI 10.1088/0305-4470/38/17/011Mosna, R.A., Hamilton, I.P., Site, L.D., Variational approach to dequantization (2006) Journal of Physics A: Mathematical and General, 39 (14), pp. L229-L235. , DOI 10.1088/0305-4470/39/14/L03, PII S0305447006181391Hamilton, I.P., Mosna, R.A., Site, L.D., Classical kinetic energy quantum fluctuation terms and kinetic-energy functionals (2007) Theor. Chem. Acct., 118, pp. 407-415Fisher, R.A., Theory of statistical estimation (1925) Proc. Cambridge Philos. Soc., 22, pp. 700-725A. Nagy, Fisher information in density functional theory (2003) J. Chem. Phys., 119, pp. 9401-9405Shannon, C.E., A mathematical theory of communication (1948) Bell Syst. Tech. J., 27, pp. 379-423. , 623-656Romera, E., Dehesa, J.S., The Fisher-Shannon information plane an electron correlation tool (2004) J. Chem. Phys., 120, pp. 8906-8912Sen, K.D., Antolín, J., Angulo, J.C., Fisher-Shannon analysis of ionization processes and isoelectronic series (2007) Phys. Rev. A, 76, p. 032502Parr, R.G., Yang, W., (1989) Density Functional Theory of Atoms and Molecules, , Oxford University Press, New YorkDreizler, R.M., Gross, E.K.U., (1990) Density Functional Theory: An Approach to the Quantum Many Body Problem, , Springer-Verlag, BerlinKoch, W., Holthausen, M.C., (2000) A Chemist's Guide to Density Functional Theory, , Wiley-VCH, WeinheimWeizsäcker, C.F.V., Zur theorie der kernmassen (1935) Z. Phys., 96, pp. 431-458Heisenberg, W., Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik (1927) Z. Phys., 43, pp. 172-198Kennard, E.H., Zur Quantenmechanik einfacher Bewegungstypen (1927) Z. Phys., 44, pp. 326-352Nelson, E., Derivation of the Schrödinger equation from Newtonian mechanics (1966) Phys. Rev., 150, pp. 1079-1085Nelson, E., (1967) Dynamical Theories of Brownian Motion, , Princeton Univ. Press, PrincetonFényes, I., Eine wahrscheinlichkeitstheoretische Begründung und Interpretation der Quantenmechanik (1952) Z. Phys., 132, pp. 81-106Weizel, W., Ableitung der Quantentheorie aus einem klassischen kausal determinierten Modell Z. Phys., 134 (1953), pp. 264-285Ableitung der Quantentheorie aus einem klassischen Modell. II (1953) Z. Phys., 135, pp. 270-273Ableitung der quantenmechanischen Wellengleichung des Mehrteilchensystems aus einem klassischen Modell (1954) Z. Phys., 136, pp. 582-604Goldstein, H., (1980) Classical Mechanics, , 2nd ed., Addison-Wesley, Reading, MAHolland, P.R., (1993) The Quantum Theory of Motion, , Cambridge University Press, CambridgeThomas, L.H., The calculation of atomic fields (1927) Proc. Cambridge Philos. Soc., 23, pp. 542-548Fermi, E., Un metodo statistico per la determinazione di alcune proprietà dell'atomo Rend (1927) Accad. Lincei, 6, pp. 602-607Yang, W., Gradient correction in Thomas-Fermi theory (1986) Phys. Rev. A, 34, pp. 4575-4585