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the [[Pressure equation |pressure]] and the [[compressibility equation]] if this superposition approximation is used to generate <math>g(r)</math>.
 
the [[Pressure equation |pressure]] and the [[compressibility equation]] if this superposition approximation is used to generate <math>g(r)</math>.
 
This approximation is rigorously correct for one-dimensional systems, and is only true in three-dimensions in the limit of zero density.  
 
This approximation is rigorously correct for one-dimensional systems, and is only true in three-dimensions in the limit of zero density.  
It has recently been shown that the Kirkwood superposition approximation precludes the existence of a critical point (Ref. 6).
 
 
==References==
 
==References==
 
#[http://dx.doi.org/10.1063/1.1749657  John G. Kirkwood, "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics '''3''' pp. 300-313 (1935)]
 
#[http://dx.doi.org/10.1063/1.1749657  John G. Kirkwood, "Statistical Mechanics of Fluid Mixtures", Journal of Chemical Physics '''3''' pp. 300-313 (1935)]
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#[http://dx.doi.org/10.1103/PhysRev.85.777 B. R. A. Nijboer and L. Van Hove "Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation", Physical Review '''85''' pp. 777 - 783  (1952)]
 
#[http://dx.doi.org/10.1103/PhysRev.85.777 B. R. A. Nijboer and L. Van Hove "Radial Distribution Function of a Gas of Hard Spheres and the Superposition Approximation", Physical Review '''85''' pp. 777 - 783  (1952)]
 
#[http://links.jstor.org/sici?sici=0080-4630%2819530122%29216%3A1125%3C203%3AOTTOF%3E2.0.CO%3B2-5 G. S. Rushbrooke and H. I. Scoins "On the Theory of Fluids", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, '''216''' pp. 203-218 (1953)]
 
#[http://links.jstor.org/sici?sici=0080-4630%2819530122%29216%3A1125%3C203%3AOTTOF%3E2.0.CO%3B2-5 G. S. Rushbrooke and H. I. Scoins "On the Theory of Fluids", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, '''216''' pp. 203-218 (1953)]
#[http://dx.doi.org/10.1063/1.4824388  Jarosław Piasecki , Piotr Szymczak  and John J. Kozak "Communication: Nonexistence of a critical point within the Kirkwood superposition approximation", Journal of Chemical Physics '''139''' 141101 (2013)]
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#[http://dx.doi.org/10.1143/PTP.21.421 Ryuzo Abe "On the Kirkwood Superposition Approximation", Progress of Theoretical Physics '''21''' pp. 421-430 (1959)]
;Related reading
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#[http://dx.doi.org/10.1063/1.1725757    Russell V. Cochran and L. H. Lund "On the Kirkwood Superposition Approximation", Journal of Chemical Physics '''41''' pp.  3499-3504 (1964)]
*[http://dx.doi.org/10.1143/PTP.21.421 Ryuzo Abe "On the Kirkwood Superposition Approximation", Progress of Theoretical Physics '''21''' pp. 421-430 (1959)]
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#[http://dx.doi.org/10.1088/0034-4885/31/2/301 G. H. A. Cole "Classical fluids and the superposition approximation", Reports on Progress in Physics '''31''' pp. 419-470 (1968)]
*[http://dx.doi.org/10.1063/1.1725757    Russell V. Cochran and L. H. Lund "On the Kirkwood Superposition Approximation", Journal of Chemical Physics '''41''' pp.  3499-3504 (1964)]
 
*[http://dx.doi.org/10.1088/0034-4885/31/2/301 G. H. A. Cole "Classical fluids and the superposition approximation", Reports on Progress in Physics '''31''' pp. 419-470 (1968)]
 
 
[[Category: Statistical mechanics]]
 
[[Category: Statistical mechanics]]

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