# What after grand canonical ensemble?

In microcanonical ensemble we have $$N$$ representative systems ($$N \rightarrow \infty)$$ characterized by macroscopic parameters $$N,V,E$$. These systems are isolated. Then we allow them to exchange energy through thermal contact and they reach equilibrium at constant temperature $$T$$ and we obtain a canonical ensemble $$N,V,T$$. Further allowing for exchanging particles we obtain grand canonical ensemble $$T,V,\mu$$. Further allowing to mechanically work on each another we should obtain at equilibrium a $$T,P,\mu$$ ensemble. Does this have a significance at all?

The theory of ensembles can be viewed from many points of view (we don't need to imagine any representative systems, for example). There are many more ensembles commonly used in physics than the microcanonical, canonical, and grand-canonical. For example there's the angular-momentum ensemble, described by Gibbs himself (Elementary Principles in Statistical Mechanics, chap. IV around eqn (98)), the pressure ensemble, eg:

the Gaussian ensemble, eg:

the evaporative ensemble, eg: