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The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s, is based upon the idea that the complicated N-electron wavefunction can be replaced with the mathematically simpler 1-electron…
In their famous paper Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of $N$ interacting electrons, albeit limited at the time by certain troubling…
Microscopic physical laws are time-symmetric, hence, a priori there exists no preferential temporal direction. However, the second law of thermodynamics allows one to associate the "forward" temporal direction to a positive variation of the…
In this article a definition of reversible processes in terms of differences in intensive Thermodynamics properties (Affinities) is proposed. This definition makes it possible to both define reversible processes before introducing the…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
Recently there has been considerable interest in the Fluctuation Theorem (FT). The FT shows how time reversible microscopic dynamics leads to irreversible macroscopic behavior as the system size or observation time increases. We show that…
Irreversible phenomena, such as the production of entropy and heat, arise from fundamental reversible dynamics because the forward dynamics is too complex, in the sense that it becomes impossible to provide the necessary information to keep…
While in principle, finite temperature density functional theory (ftDFT) should be a powerful tool for the study of crystallization, in practice this has not so far been the case. Progress has been hampered by technical problems which have…
This article is a rough, quirky overview of both the history and present state of the art of density functional theory. The field is so huge that no attempt to be comprehensive is made. We focus on the underlying exact theory, the origin of…
Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example. to calculate the density distribution of the molecules in the…
Using dynamical density functional theory (DDFT) methods we investigate the laning instability of a sheared colloidal suspension. The nonequilibrium ordering at the laning transition is driven by non-affine particle motion arising from…
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…
The paper sets forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTD), developed by the author during the last decade and spread over series of publications. Based on the linear equations of irreversible…
We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear…
Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope,…
Fluctuation theorems are fundamental results in non-equilibrium thermodynamics. Considering the fluctuation theorem with respect to the entropy production and an observable, we derive a new thermodynamic uncertainty relation which also…
This review is based on lectures given by the author at the Enrico Fermi Summer School in Varenna. It presents the basics of Density Functional Theory (DFT) for Fermi superfluids, with particular emphasis on nuclear systems. Special…
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems…
Real-time time-dependent density functional theory (TDDFT) is widely considered to be the most accurate available method for calculating electronic stopping powers from first principles, but there have been relatively few assessments of the…
Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary…