Questions about metastable van der Waals states This is an excerpt from David Tong's Statistical Physics:

My questions:

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*Are those metastable states ("good states") taken from the Maxwell-corrected $pV$-curves (flat lines) or from the uncorrected $pV$-curves as in the figure?

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*If they are referring to the down-going segments between the co-existence curve and the spinodal curve in the figure, how are they connected to the flat lines inside the spinodal region after correction? (The $pV$-curves will be discontinuous.)



*Any references for the free energy calculation in metastability and the comparison with the free energy in equilibrium?

 A: 
Are those metastable states ("good states") taken from the Maxwell-corrected -curves (flat lines) or from the uncorrected -curves as in the figure?

The van der Waals metastable states are precisely the uncorrected down-going segments between the co-existence and spinodal curves in the figure. If one traced the flat coexistence part of the isotherms, these segments would lay below (at low volumes) and above it (at high volumes). The metastable states end at the spinodal curve.

Any references for the free energy calculation in metastability and the comparison with the free energy in equilibrium?

There are different ways to calculate the free energy in the liquid and the vapor phase. Methods go from approximate variational or perturbation theories to integral equations to numerical simulations. Of course, all the numerical methods require a model for the interactions. One of the first simulation studies was the pioneering paper by Hansen, J. P., and Verlet, L. (1969). Phase transitions of the Lennard-Jones system. Physical Review, 184(1), 151.
