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An analysis shows that the ground state of the inhomogeneous system of interacting electrons in the static external field, which satisfies the thermodynamic limit, can be consistently described only using the Green function theory based on…
The partition function, $U$, the number of available states in an atom or molecules, is crucial for understanding the physical state of any astrophysical system in thermodynamic equilibrium. There are surprisingly few {\em useful}…
It is shown that the partial temperatures of a homogeneous multicomponent gas mixture in the thermodynamical equilibrium cannot be equal to each other. New general solutions for equilibrium distribution functions of the multicomponent…
We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density,…
We construct a new class of phenomenological equations of state for homogeneous matter for use in simulations of hot and dense matter in local thermodynamic equilibrium. We construct a functional form which respects experimental,…
Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…
Many references exist in the density functional theory (DFT) literature to the chemical potential of the electrons in an atom or a molecule. The origin of this notion has been the identification of the Lagrange multiplier $\mu = \partial…
The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
An alternative type of approximation for the exchange and correlation functional in density functional theory is proposed. This approximation depends on a variable $u$ that is able to detect inhomogeneities in the electron density $\rho$…
To the student of thermodynamics the most difficult subject is entropy. In this paper we examine the actual, practical application of entropy to two simple systems, the homogeneous slab with fixed boundary values of the temperature, and an…
A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation…
We compare dynamical heterogeneities in equilibrated supercooled liquids and in the nonequilibrium glassy state within the framework of the random first order transition theory. Fluctuating mobility generation and transport in the glass are…
Based on our derivation of finite temperature reduced density matrix functional theory and the discussion of the performance of its first-order functional this work presents several different correlation-energy functionals and applies them…
We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…
Extending the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistics of a hydrogen atom in a uniform magnetic at all temperatures. The zero-temperature…
Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic…
In this short note, we present some work on investigating electron temperatures and potentials in steady or unsteady dilute plasma flows. The analysis is based on the detailed fluid model for electrons. Ionization, normalized electron…
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…
Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal or macromolecular system in the strong damping limit the most likely path for nucleation can be determined by gradient…