相关论文: Free energy of disordered urn models in the canoni…

A theoretical model for polydisperse systems of hard spheres is said to be truncatable when the excess free energy depends on the size distribution through a finite number $K$ of moments. This Note proves an exact scaling relation for…

Motivated by the design question of additional fuel needed to complete a task in an uncertain environment, this paper introduces metrics to quantify the maximal additional energy used by a control system in the presence of bounded…

Estimating the free energy in molecular simulation requires, implicitly or explicitly, counting how many times the system is observed in a finite region. If the simulation is biased by an external potential, the weight of the configurations…

Consider the multicolored urn model where, after every draw, balls of the different colors are added to the urn in a proportion determined by a given stochastic replacement matrix. We consider some special replacement matrices which are not…

We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We…

We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model…

We propose a new method to compute the free energy or enthalpy of fluids or disordered solids by computer simulation . The main idea is to construct a reference system by freezing one representative configuration, and then carry out a…

We show that the asymptotic iteration method converges and yields accurate energies for a perturbed Coulomb model. We also discuss alternative perturbation approaches to that model.

We complete the study of the model introduced in [11]. It is a two-color urn model with multiple drawing and random (non-balanced) time-dependent reinforcement matrix. The number of sampled balls at each time-step is random. We identify the…

We introduce a mean field spin glass model with gaussian distribuited spins and pairwise interactions, whose couplings are drawn randomly from a normal gaussian distribution too. We completely control the main thermodynamical properties of…

We investigate large deviations of the free energy in the O'Connell-Yor polymer through a variational representation of the positive real moment Lyapunov exponents of the associated parabolic Anderson model. Our methods yield an exact…

We study the infinite urn scheme when the balls are sequentially distributed over an infinite number of urns labelled 1,2,... so that the urn $j$ at every draw gets a ball with probability $p_j$, $\sum_j p_j=1$. We prove functional central…

The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid state systems. However, the simultaneous occurence of quantum, correlation, and thermal effects makes the theoretical description…

Sets of free energy differences are useful for finding the equilibria of chemical reactions, while absolute free energies have little physical meaning. However finding the relative free energy between two macrostates by subtraction of their…

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…

We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi…

An urn model of Diaconis and some generalizations are discussed. A convergence theorem is proved that implies for Diaconis' model that the empirical distribution of balls in the urn converges with probability one to the uniform…

We use Kaufman's spinor method to calculate the bulk, surface and corner free energies $f_b, f_s, f_s', f_c$ of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For $f_b, f_s, f'_s$ our results of…

Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is…

The free energy of a nonabelian gauge theory at high temperature $T$ can be calculated to order $g^5$ using resummed perturbation theory, but the method breaks down at order $g^6$. A new method is developed for calculating the free energy…