Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-08-29
Physica A387, 6759 (2008)
Physics
Condensed Matter
Statistical Mechanics
5 figures, accepted for publication in Physica A, 2008
Scientific paper
10.1016/j.physa.2008.08.035
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions, and (b) to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry. As an illustration we apply our method to simple fluids. The "exact" canonical distribution is approximated by that of a fluid of hard spheres. The proposed method first determines the preferred value of the hard-sphere diameter, and then obtains an optimal hard-sphere approximation by a suitably weighed average over different hard-sphere diameters. This leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a numerical demonstration, the radial distribution function and the equation of state for a Lennard-Jones fluid (argon) are compared with results from molecular dynamics simulations.
Caticha Ariel
Tseng Chih-Yuan
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