Related papers: Variational Principle of Classical Density Functio…

We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random…

We establish one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at an elevated temperature. Including temperature guarantees differentiability of the universal functional by occupying all…

Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…

For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order…

A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function…

We present the theoretical analysis of the steady state currents and density distributions of particles moving with Langevin dynamics, under the effects of an external potential displaced at constant rate. The Dynamic Density Functional…

We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection…

We present an alternative derivation of the dynamical density functional theory for the one body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation elucidates further…

A theory is developed for magnetically confined Fermi gas at low temperature based on the density functional theory. The theory is illustrated by numerical calculation of density distributions of Fermi atoms $^{40}$K with parameters…

We derive the Planck law from a classical variational principle over probability densities, without invoking quantum states, quantized oscillator energies, or ensemble averages. We construct a generalized free energy functional involving…

A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…

The issue of discrete probability estimation for samples of small size is addressed in this study. The maximum likelihood method often suffers over-fitting when insufficient data is available. Although the Bayesian approach can avoid…

We present a metric-space approach to quantify the performance of density-functional approximations for interacting many-body systems and to explore the validity of the Hohenberg-Kohn-type theorem on fermionic lattices. This theorem…

The density functional theory is extended to account for self-bound systems. To this end the Hohenberg-Kohn theorem is formulated for the intrinsic density and a Kohn-Sham like procedure for an $N$--body system is derived using the…

Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…

The electron density $n(\rb,t)$, which is the central tool of time-dependent density functional theory, is presently considered to be derivable from a one-body time-dependent potential $V(\rb,t)$, via one-electron wave functions satisfying…

For a many-electron system, whether the particle density $\rho(\mathbf{r})$ and the total current density $\mathbf{j}(\mathbf{r})$ are sufficient to determine the one-body potential $V(\mathbf{r})$ and vector potential…

The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We…

We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…

We investigate and exploit consequences of the recent neural metadensity functional theory [Kampa et al., Phys. Rev. Lett. 134, 107301 (2025), 10.1103/PhysRevLett.134.107301] for describing the physics of inhomogeneous fluids. The…