The Ornstein-Zernike equation in the canonical ensemble
Departamento de Física Aplicada,
Facultad de Ciencias
Universidad de Salamanca - 37008 Salamanca, Spain
Accepted: 12 March 2001
A general density-functional formalism using an extended variable space is presented for classical fluids in the canonical ensemble (CE). An exact equation that plays the role of the Ornstein-Zernike (OZ) equation in the grand canonical ensemble (GCE) is derived in the CE. When applied to the ideal gas we obtain the exact result for the total correlation function hN. In the case of the homogeneous fluid with N particles, the new equation only differs from OZ by 1/N and it allows us 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.
PACS: 61.20.Gy – Theory and models of liquid structure / 05.20.Gg – Classical ensemble theory
© EDP Sciences, 2001