I believe that the pressure for these systems cannot be introduced because of absence of local equilibrium. In our paper

Melkikh A.V., Melkikh E.A. Can we use thermodynamics in the systems with gravity? Modern Physics Letters B, (2017).

it was shown, that the term "pressure" is fundamentally connected to the existence of local equilibrium and cannot be introduced without it.

Article Can we use thermodynamics in the systems with gravity?

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