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The density-functional (DF) theory provides a simple method for calculating the properties of an interacting system under an external potential by associating it with a corresponding non-interacting system. Here, we find some relations in…

We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by…

We prove convergence of the multi-body correlation function as a power series in the density. We work in the context of the cluster expansion in the canonical ensemble and we obtain bounds uniform in the volume and the number of particles.…

Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…

One of the most powerful strategies to address properties of real many-body systems is to incorporate data obtained for models, for example, to use data of the homogeneous electron gas in order to build the Local Density Approximation for…

We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double…

We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling…

We provide an extended acount of the recent statistical mechanical theory of gauge invariance against operator shifting in quantum many-body systems (arXiv:2509.20494). The gauge transformation is enacted by a shifting superoperator that…

Density Functional Theory relies on universal functionals characteristic of a given system. Those functionals in general are different for the electron gas and for jellium (electron gas with uniform background). However, jellium is…

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard…

Density functional theory has made great success in solid state physics, quantum chemistry and in computational material sciences. In this work we show that density functional theory could shed light on phase transitions and entanglement at…

A logical foundation of equilibrium state density functional theory in a Kohn-Sham type formulation is presented on the basis of Mermin's treatment of the grand canonical state. it is simpler and more satisfactory compared to the usual…

The molecular density functional theory of fluids provides an exact theory for computing solvation free energies in implicit solvents. One of the reasons it has not received nearly as much attention as quantum density functional theory for…

This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in…

Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE). However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in…

Finite temperature density functional theory provides, in principle, an exact description of the thermodynamical equilibrium of many-electron systems. In practical applications, however, the functionals must be approximated. Efficient and…

Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and…

The thermodynamics of the inhomogeneous one-dimensional repulsive fermionic Hubbard model with parabolic confinement is studied by a density-functional theory approach, based on Mermin's generalization to finite temperatures. A…

Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence…

In this chapter, we discuss recent advances and new opportunities through methods of machine learning for the field of classical density functional theory, dealing with the equilibrium properties of thermal nano- and micro-particle systems…