Abstract
The study of one-dimensional hard rods with gravitational interactions was made by means of the isobaric and the canonical ensembles. The canonical partition function was obtained from the isobaric partition function by taking the inverse Laplace transform. The explicit closed forms for the canonical particle density and the higher-order molecular distribution functions were determined. The wall pressures, where the force exerted on the fluid by the walls, were obtained from both the partial derivative of the free energy with respect to the position of the walls and the contact value of the density determined from the one-particle density at the walls. The wall pressure implies that the hard rods with a gravitational interaction do not exhibit a phase transition. The partition function and the molecular distribution functions in the grand canonical ensemble are also reported.
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Jang, S., Shin, G.R. & Kim, SC. One-Dimensional model of hard rods with gravitational interactions. Journal of the Korean Physical Society 70, 673–681 (2017). https://doi.org/10.3938/jkps.70.673
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DOI: https://doi.org/10.3938/jkps.70.673