Abstract
The exact statistical mechanics of the one-dimensional classical hard-rod mixtures in an external field is reformulated. For any number of components and arbitrary size distribution, the problem is reduced to solving only two auxiliary functions. The component density profiles, thermodynamic properties, and correlation functions are all explicit functionals of these two functions. Application is made to study the size selectivity of a hard-rod mixture, with a uniform size distribution, confined between hard walls. Approximate theories for inhomogeneous three-dimensional fluid mixtures, based on simple generalizations of the exact results in one dimension, are discussed.
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