Translational Invariance Properties of a Finite One-Dimensional Hard-Core Fluid

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Abstract
A formalism is developed for expressing the n‐particle distribution functions Dn(x1 ≤ x2 ≤ … ≤ xn) explicitly in terms of the configurational partition function for one‐dimensional fluids with hard‐core repulsive and nearest‐neighbor attractive forces. The translational invariance properties of the Dn functions are investigated for the case of no attractive forces when the system is finite. When the number density is less than half the close packing density, there exists a central region in which D1(x) is constant and all the Dn functions, n ≥ 2, are functions of the (n−1) nearest‐neighbor separation distances. Several relevant theorems are proved and limiting cases are investigated.

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