Related papers: Free energy calculation of crystalline solids usin…
The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory. The goal here is to extend and complete an…
In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by…
We present a new approach to analyze homogeneous nucleation based on non-equilibrium thermodynamics. The starting point is the formulation of a Gibbs equation for the variations of the entropy of the system, whose state is characterized by…
Several research groups have recently reported {\em ab initio} calculations of the melting properties of metals based on density functional theory, but there have been unexpectedly large disagreements between results obtained by different…
Energy-based models (EBMs) are flexible generative architectures inspired by statistical physics, but their learning and generative properties remain poorly understood. Here, we analyze a solvable EBM in the high-dimensional limit: the…
Atomic-scale phase-field modeling formulates the probability densities of atomic vibrations as Gaussian distributions and derives a free energy functional using variational Gaussian theory and interatomic potentials. This framework permits…
A simple technique is proposed for numerically determining equilibrium ion distribution functions belonging to free energies of the Poisson-Boltzmann type. The central idea is to perform a conventional Monte-Carlo simulation using the free…
Using a thermodynamic integration scheme, we compute the free energy cost per unit area, $\gamma$, of forming an interface between a crystal and a frozen structured wall, formed by particles frozen into the same equilibrium structure as the…
Sampling from unnormalized target distributions, e.g.\ Boltzmann distributions $\mu_{\text{target}}(x) \propto \exp(-E(x)/T)$, is fundamental to many scientific applications yet computationally challenging due to complex, high-dimensional…
We prove Goldschmidt's formula [Phys. Rev. B 47 (1990) 4858] for the free energy of the quantum random energy model. In particular, we verify the location of the first order and the freezing transition in the phase diagram. The proof is…
The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the…
We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three body potential. The free energy barriers to crystallisation are computed using umbrella sampling…
We present a method for determining the free energy of coexisting states from irreversible work measurements. Our approach is based on a fluctuation relation that is valid for dissipative transformations in partially equilibrated systems.…
This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy…
We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy…
Computational modeling is an integral part of catalysis research. With it, new methodologies are being developed and implemented to improve the accuracy of simulations while reducing the computational cost. In particular, specific…
We combine machine learning (ML) with Monte Carlo (MC) simulations to study the crystal nucleation process. Using ML, we evaluate the canonical partition function of the system over the range of densities and temperatures spanned during…
We analyze free energy and specific heat for fermions interacting with gapless bosons at a quantum-critical point (QCP) in a metal. We use the Luttinger-Ward-Eliashberg formula for the free energy in the normal state, which includes…
A melting transition for a system of hard spheres interacting by a repulsive Yukawa potential of DLVO form is studied. To find the location of the phase boundary, we propose a simple theory to calculate the free energies for the coexisting…
We develop a method to fit high-temperature Gibbs free energy data for the development of interatomic potentials for atomic systems. The approach is based on Hamiltonian thermodynamic integration, enabling the identification of suitable…