Abstract
The Gibbsian N-body density function of a Hamiltonian H N that is rotationally and translationally invariant must itself be rotationally and translationally invariant, as must then also be all reduced n-body density functions of this Hamiltonian. In particular, the one-body density is a constant and the two-body density depends only on relative coordinates. An external field destroys this homogeneity, producing anisotropy or nonuniformity [1, 2], and so makes necessary the joint calculation of the coupled one-body and two-body density functions. A striking if familiar example of the response of a bulk system to an external field is ferromagnetism. We shall use this particular case here to present a general procedure to compute the coupled one-body and two-body density functions of an inhomogeneous classical fluid in an external field. Remarkably, the procedure is no more difficult to carry through than similar calculations for ordinary homogeneous systems.
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