Exact conditions on the temperature dependence of density functionals

Abstract

Universal exact conditions guided the construction of most ground-state density functional approximations in use today. We derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.

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• Nonempirical Semi-local Free-Energy Density Functional for Matter Under Extreme Conditions
• \emph{Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas
• Finite temperature Green's function approach for excited state and thermodynamic properties of cool to warm dense matter
• The Relevance of Electronic Perturbations in the Warm Dense Electron Gas
• Benchmarking Exchange-Correlation Functionals in the Spin-Polarized Inhomogeneous Electron Gas under Warm Dense Conditions
• Free Energy of the Uniform Electron Gas: Testing Analytical Models against First Principle Results
• Effective mass of quasiparticles from thermodynamics
• First-principles derivation and properties of density-functional average-atom models
• Hohenberg-Kohn theorems for interactions, spin and temperature
• Development of the temperature-dependent interatomic potential for molecular dynamics simulation of metal irradiated with an ultrashort pulse laser
• Machine learning the electronic structure of matter across temperatures
• Thermal stitching: Extending the reach of quantum fermion solvers
• Entropic Density Functional Theory
• Exchange-correlation entropy from the generalized thermal adiabatic connection
• Approximating quantum thermodynamic properties using DFT
• Kinetic correlation functionals from the entropic regularisation of the strictly-correlated electrons problem
• Full Quantum Work Statistics for Non-Homogeneous Many-Body Systems
• Warming Up Density Functional Theory
• v-Representability on a one-dimensional torus at elevated temperatures
• Finite-Temperature Thermally-Assisted-Occupation Density Functional Theory, Ab Initio Molecular Dynamics, and Quantum Mechanics/Molecular Mechanics Methods