Related papers: Bridging the gap between correlation entropy funct…

In this paper we extend the familiar continuum electrostatic model with a perturbation to the usual macroscopic boundary condition. The perturbation is based on the mean spherical approximation (MSA), to derive a multiscale hydration-shell…

Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility…

We develop a generalized hyperdynamics method, which is able to simulate slow dynamics in atomistic general (both energy and entropy-dominated) systems. We show that a few functionals of the pair correlation function, involving two-body…

The past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. While…

This paper presents a unified method for formulating a field-theoretic perturbation theory that encompasses the conventional liquid state theory. First, the free-energy functional of instantaneous correlation field is obtained from the…

The hierarchical reference theory (HRT) and the self-consistent Ornstein-Zernike approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as the phase…

We develop a framework of canonical correlation analysis for distribution-valued functional data within the geometry of Wasserstein spaces. Specifically, we formulate an intrinsic concept of correlation between random distributions, propose…

We study the glassy transition for simple liquids in the hypernetted chain (HNC) approximation by means of an effective potential recently introduced. Integrating the HNC equations for hard spheres, we find a transition scenario analogous…

We present a unifying approach to the study of entropies in Mathematics, such as measure entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account discrete dynamical systems, that is, pairs $(X,T)$, where…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

In important early work, Stell showed that one can determine the pair correlation function h(r) of the hard sphere fluid for all distances r by specifying only the "tail" of the direct correlation function c(r) at separations greater than…

We use the entropy production variational method to associate a one particle distribution function to the assumed known energy-momentum and entropy currents describing a relativistic conformal fluid. Assuming a simple form for the collision…

We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise…

The prominence of density functional theory (DFT) in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron…

We present a rigorous framework that combines single-particle Green's function theory with density functional theory based on a separation of electron-electron interactions into short-range and long-range components. Short-range…

The leading correction to the smoothed connected energy density-density correlation function is obtained for the large energy difference, within the context of the Gaussian Random Matrix Theory. In order to achieve this result, the…

We investigate the value of the correlation function of an inhomogeneous hard-sphere fluid at contact. This quantity plays a critical role in Statistical Associating Fluid Theory (SAFT), which is the basis of a number of recently developed…

The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets.…

The neural collapse (NC) phenomenon describes an underlying geometric symmetry for deep neural networks, where both deeply learned features and classifiers converge to a simplex equiangular tight frame. It has been shown that both…

We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating…