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I think it may not be possible.

Given all the pair correlation functions, it seems possible to obtain the internal energy (assuming different species interact through pair-potentials (i.e. potentials that do not involve more than two bodies)).

To obtain the free energy, the "naive" way is to obtain the partition function and take logarithm. Yet it seems not easy (except possibly through cluster expansions? which is not exact.)

Any help will be much appreciated.

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