Expression in Terms of Molecular Distribution Functions for the Entropy Density in an Infinite System

Abstract

An expression for the entropy in a finite subvolume of an infinite fluid, originally proposed by Strato-novich on the basis of information theory, is rewritten in terms of functions related to the potentials of average force. The result exhibits a correction to the corresponding expression obtained by H. S. Green for a finite system, in the form of a series in powers of the concentration, of which the first terms have been investigated by Richardson. By neglect of correlations of three or more molecules and powers of the density higher than the third, the result is specialized to the case of a gas of low density, for which the configurational entropy per molecule is calculated with use of the radial distribution obtained by Kirkwood for hard-sphere and hard-core Lennard-Jones potentials.