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In computational mechanics and statistical mechanics, a radial distribution function (RDF), g(r), describes how the density of surrounding matter varies as a function of the distance from a distinguished point. This is normalized by the average density such that the function goes to 1 far from the distinguished point when the medium is even slightly disordered. If, for example, we choose to locate our distinguished point at the center of a hard-core particle with radius σ, g(r) will be 0 for r < σ.
Given a potential energy function, the radial distribution function can be found via sampling -- see statistical mechanics.
What makes the RDF important is that for certain systems it can be used to calculate most thermodynamically interesting quantities, such as the average energy U or entropy S.
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