Maximum Entropy and the Variational Method in Statistical Mechanics: an Application to Simple Fluids
| dc.creator | Tseng, Chih-Yuan | |
| dc.creator | Caticha, Ariel | |
| dc.date | 2004-11-25 | |
| dc.date | 2007-07-24 | |
| dc.date.accessioned | 2026-07-07T08:19:44Z | |
| dc.date.available | 2026-07-07T08:19:44Z | |
| dc.description | 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. | |
| dc.description | 5 figures. Additional demonstrations on radial distribution functions and equation of states are added | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0411625 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0411625 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134865 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Maximum Entropy and the Variational Method in Statistical Mechanics: an Application to Simple Fluids | |
| dc.type | text |