2004/11/25 by Chih‐Yuan Tseng, Tseng, Chih-Yuan, Ariel Caticha +1 · 1 citation
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Phase Equilibria and Thermodynamics #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.cond-mat/0411625
openalex publication_date 2004/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the method of Maximum Entropy (ME) as a technique to generate approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a "best" approximation from within a family of trial distributions, and (b) to quantify the extent to which non-optimal trial distributions are ruled out. The Bogoliuvob variational method is shown to be included as a special case. As an illustration we apply our method to simple fluids. In a first use of the ME method the "exact" canonical distribution is approximated by that of a fluid of hard spheres and ME is used to select the optimal value of the hard-sphere diameter. A second, more refined application of the ME method approximates the "exact" distribution by a suitably weighed average over different hard-sphere diameters and leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a specific example, the radial distribution function and the equation of state for a Lennard-Jones fluid (Argon) are compared with results from molecular dynamics simulations.