Inquiry on mu-P-T ensemble

A µ-P-T ensemble isn't a real thermodynamical ensemble. You can figure
that out if you consider the relation of µ and P in an ideal gas.

Yes mu-p-T is not a thermodynamic ensemble. However, LAMMPS does not forbid it. There are two problems:

1. This combination has not been tested *at all*
2. There is no fixed extensive quantity (N or V or E), so the system is free to grow or shrink with any constraint.

However, if you introduced a second species that is not exchanged, you can run mu1-N2-p-T dynamics. This is a thermodynamic ensemble, and can be used to study polymer swelling, etc. It does not suffer from Problem 2, but Problem 1 is still a concern.