Related papers: Jarzynski equality for the Jepsen gas
In this paper, we consider the 3-D steady potential flow for a compressible gas with pressure satisfying $p'(\rho)=\rho^{\gamma-1}$, where $\rho$ is the density and $\gamma\geq-1$ is a constant. In spherical coordinates, the potential…
The Generalized Slater-Jastrow trial functional is a modification of the Slater-Jastrow functional where, effectively, the argument of the Jastrow factor can be momentum dependent. The associated Euler equations, which provide an…
Recent years have witnessed major advances in our understanding of nonequilibrium processes. The Jarzynski equality, for example, provides a link between equilibrium free energy differences and finite-time, nonequilibrium dynamics. We…
The equations of motion for the variance of strictly one-dimensional or two-dimensional non-relativistic fireballs are derived, from the hydrodynamic equations for an ideal, structureless Boltzmann gas. For this purpose a Gaussian number…
An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is…
We study the polaron quasiparticle in a one-dimensional Bose gas. In the integrable case described by the Yang-Gaudin model, we derive an exact result for the polaron mass in the thermodynamic limit. It is expressed in terms of the…
We study the extremal dynamics emerging in an out-of-equilibrium one-dimensional Jepsen gas of $(N+1)$ hard-point particles. The particles undergo binary elastic collisions, but move ballistically in-between collisions. The gas is initally…
A general density-functional formalism using an extended variable-space is presented for classical fluids in the canonical ensemble (CE). An exact equation is derived that plays the role of the Ornstein-Zernike (OZ) equation in the grand…
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using…
The long-time solutions of the Galerkin-truncated three-dimensional, incompressible Euler equation relax to an absolute equilibrium as a consequence of phase space and kinetic energy conservation in such a finite-dimensional system. These…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
Jarzynski's equality [1] allows us to investigate free energy landscapes (FELs) by constructing distributions of work performed on a system from an initial ensemble of states to final states. This work is experimentally measured by…
The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be $\lambda=1.5.$ In particular, for both fluids we…
We investigate, by "a la Marcinkiewicz" techniques applied to the (asymptotic) density function, how dense systems of equal spheres of $\rb^{n}, n \geq 1,$ can be partitioned at infinity in order to allow the computation of their density as…
We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle…
The influence of a curved spacetime $M$ on the physical behavior of an ideal gas of $N$ particles is analyzed by considering the phase space of the system as a region of the cotangent bundle $T^{*}M^{N}$ and using Souriau's Lie group…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
We consider the $J/\Psi$ suppression at a high energy heavy ion collision. An ideal gas of massive hadrons in thermal and chemical equilibrium is formed in the central region. The finite-size gas expands longitudinally in accordance with…
The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…
Based on accurate Lennard-Jones type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in…