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Entropic Density Functional Theory
Version 1
: Received: 22 November 2023 / Approved: 4 December 2023 / Online: 4 December 2023 (06:58:45 CET)
A peer-reviewed article of this Preprint also exists.
Yousefi, A.; Caticha, A. Entropic Density Functional Theory. Entropy 2024, 26, 10. Yousefi, A.; Caticha, A. Entropic Density Functional Theory. Entropy 2024, 26, 10.
Abstract
A formulation of the Density Functional Theory (DFT) is constructed as an application of the method of maximum entropy for an inhomogeneous fluid in thermal equilibrium. The use of entropy as a systematic method to generate optimal approximations is extended from the classical to the quantum domain. This process introduces a family of trial density operators that are parametrized by the particle density. The optimal density operator is that which maximizes the quantum entropy relative to the exact canonical density operator. This approach reproduces the variational principle of DFT and allows a simple proof of the Hohenberg-Kohn theorem at finite temperature. Finally, as an illustration, we discuss the Kohn-Sham approximation scheme at finite temperature
Keywords
density functional theory; Hohenberg-Kohn theorem; entropic inference; method of maximum entropy; inhomogeneous fluids
Subject
Physical Sciences, Condensed Matter Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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