Is there Ornstein-Zernike equation in the canonical ensemble?
J. A. White, S. Velasco
Abstract
A general density-functional formalism using an extended variable-space is presented for classical fluids in the canonical ensemble (CE). An exact equation is derived that plays the role of the Ornstein-Zernike (OZ) equation in the grand canonical ensemble (GCE). When applied to the ideal gas we obtain the exact result for the total correlation function hN. For a homogeneous fluid with N particles the new equation only differs from OZ by 1/N and it allows to obtain an approximate expression for hN in terms of its GCE counterpart that agrees with the expansion of hN in powers of 1/N.
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