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Here post your question It is well-known that Parrinello Rahman coupling can lead to fluctuations in box volumes which is why it is not recommended for equilibration runs. However it is usually fine for production runs. See:
Likewise it is known that for inhomegeneous system it may be necessary to use Lennard-Jones PME, see
https://pubs.acs.org/doi/10.1021/ct400140n
In a recent simulation of a pure liqud we found that LJ-PME was needed to get a stable system with PR coupling since the liquid was close to a phase transition, that is not a spatial homogeneity but a temporal homogeneity. This i documented as a gitlab issue here including graphs and example inputs.