Chih-Yuan Tseng, Ariel Caticha
Published 2003-10-30Version 2
We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard spheres; ME is used to select an optimal value of the hard-sphere diameter. These results coincide with the results obtained using the Bogoliuvob variational method. A second more complete use of the ME method leads to a better descritption of the soft-core nature of the interatomic potential in terms of a statistical mixture of distributions corresponding to hard spheres of different diameters. As an example, the radial distribution function for a Lennard-Jones fluid (Argon) is compared with results from molecular dynamics simulations. There is a considerable improvement over the results obtained from the Bogoliuvob principle.
Comments: 14 pages and 4 figures. Presented at MaxEnt 2003, the 23rd International Workshop on Bayesian Inference and Maximum Entropy Methods (August 3-8, 2003, Jackson Hole, WY, USA)
Journal: p. 17 in "Bayesian Inference and Maximum Entropy Methods in Science and Engineering" ed. by G. Erickson and Y. Zhai (A.I.P. Vol. 707, 2004)
On the radial distribution function of a hard-sphere fluid
Velocity and energy distributions in microcanonical ensembles of hard spheres
Condensation of Hard Spheres Under Gravity
