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Author Tseng, Chih-Yuan ♦ Caticha, Ariel
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-08-29
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics
Subject Keyword Condensed Matter - Statistical Mechanics ♦ Computer Science - Information Theory ♦ Mathematics - Probability ♦ Statistics and Probability ♦ Physics - Data Analysis ♦ cs ♦ math ♦ physics:cond-mat ♦ physics:physics
Abstract 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.
Description Comment: 5 figures, accepted for publication in Physica A, 2008
Reference: Physica A387, 6759 (2008)
Educational Use Research
Learning Resource Type Article


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