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I have found textbooks/paper which discuss the pair-correlation function of molecules which are influenced by the Lennard-Jones potential. This gives a direct method for obtaining the various macroscopic properties of the substance such as internal energy and pressure.

However, I am unable to locate material which derives expressions related to the miscibility gap when two Lennard-Jones fluids are mixed together $\textit{starting from}$ the fundamental interaction potentials or the pair-correlation function. Can anyone suggest good reading material in this regard?

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