相关论文: Cavity volume and free energy in many-body systems

Results from spectral geometry such as Weyl's formula can be used to relate the thermodynamic properties of a free massless field to the spatial manifold on which it is defined. We begin by calculating the free energy in two cases:…

We consider a binary system of small and large spheres of finite size in a continuous medium interacting via a non-negative potential. We work in the canonical ensemble and compute upper and lower bound for the free energy at finite and…

We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is taken also as the thermal bath so that the system thermalizes by collisions…

The thermodynamics for a system with given temperature, density, and volume is described by the Canonical ensemble. The thermodynamics for a corresponding system with the same temperature, volume, and average density is described by the…

We present the full thermodynamics of a fluid confined by an arbitrary external potential based on the virial expansion of the grand potential. The fluid may be classical or quantum and it is assumed that interatomic interactions are…

Approach to the thermodynamic limit of a non-relativistic ideal gas in a periodic box is investigated. The single particle wave function obeys twisted boundary condition, $\psi(L)=e^{i\theta}\psi(0)$ for which the free particle spectrum is…

We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are 'available-volume' and 'free-volume' methods. We add a third one, which we call…

This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object.…

We have obtained an exact expression for the phase-space volume corresponding to a microcanonical ensemble of systems under center of mass, total linear and angular momenta conservation constraints, and arbitrary constraints on the…

We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e. the volume of space that a sphere can explore without touching another…

We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any…

We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported…

The aim of this paper is twofold: - To give an elementary and self-contained proof of an explicit formula for the free energy for a general class of polymer chains interacting with an environment through periodic potentials. This…

This paper determines the excess free energy associated with the formation of a spherical cavity in a hard sphere fluid. The solvation free energy can be calculated by integration of the structural changes induced by inserting the cavity…

The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the Density Functional Theory, are reformulated in terms of a particular many-body density, which is translational invariant and therefore is relevant for…

The thermodynamics framework of an interacting quantum gas trapped by an arbitrary external potential is reviewed. We show that for each confining potential, in the thermodynamic limit, there emerge "generalized" volume and pressure…

We have considered a model of a small finite system with internal particles and surface degrees of freedom. All the main statistical distributions were explicitly obtained, on a pre thermodynamic limit basis. The concept of temperature or…

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…

We consider dimer model on a hexagonal lattice. This model can be seen as a "pile of cubes in the box". The energy of configuration is given by the volume of the pile and the partition function is computed by the classical MacMahon formula…

We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…