Entropic Density Functional Theory.

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Condensed matter physics

Background:

• Density Functional Theory (DFT) is a powerful quantum mechanical method for electronic structure calculations.
• The method of maximum entropy is a powerful tool for constructing probability distributions and approximations.
• Understanding systems in thermal equilibrium is crucial in many areas of physics and chemistry.

Purpose of the Study:

• To formulate a density functional theory (DFT) approach using the method of maximum entropy.
• To extend the application of maximum entropy from classical to quantum systems.
• To provide a new derivation of the Hohenberg-Kohn theorem at finite temperatures.

Main Methods:

• Constructing a formulation of DFT based on maximum entropy.
• Introducing trial density operators parameterized by particle density.
• Maximizing quantum entropy relative to the exact canonical density operator.

Main Results:

• The proposed approach reproduces the variational principle of DFT.
• A simple proof of the Hohenberg-Kohn theorem at finite temperature is achieved.
• The Kohn-Sham approximation scheme at finite temperature is discussed as an illustration.

Conclusions:

• The maximum entropy method offers a systematic way to generate optimal approximations in quantum DFT.
• This formulation provides a robust theoretical framework for finite-temperature DFT calculations.
• The approach offers new insights into the foundations of DFT and its applications.