While teaching statistical mechanics, and describing the common thermodynamic ensembles (microcanonical, canonical, grand canonical), I usually give a line on why there can be no $(\mu, P, T)$ thermodynamic ensemble ($\mu$ being the chemical potential, $P$ being the pressure, and $T$ being the temperature). My usual explanation is a handwaving that all of the control parameters would be intensive, which leaves all the extensive conjugated parameters unbounded, and you can't write your sums and integrals anymore.

However, I have always felt uneasy because:

1. I never was able to properly convince myself where exactly the problem arose in a formal derivation of the ensemble (I am a chemist and as such, my learning of statistical mechanics didn't dwell on formal derivations).

2. I know that the $(\mu, P, T)$ can actually be used for example for numerical simulations, if you rely on limited sampling to keep you out of harm's way (see, for example, [F. A. Escobedo, *J. Chem. Phys.*, 1998](http://dx.doi.org/doi:10.1063/1.476429)). (Be sure to call it a *pseudo-ensemble* if you want to publish it, though.)

So, I would like to ask how to address point #1 above: **how can you properly demonstrate how chaos would arise from the equations of statistical mechanisms if one defines a $(\mu, P, T)$ ensemble?**