I have recently learned about ensembles in statistical mechanics, and I've seen multiple applications and interpretations of the EVN (microcanonical), TVN (canonical), $\mu$VT (grand canonical) and NPT (isothermal isobaric) ensembles, I've also learned that the $\mu$PT ensemble doesn't exist. What happens with the $\mu$VE ensemble? is it possible to postulate it? can there be a system that exchanges particles with its surroundings but its energy is fixed? I find it hard to come up with a physical way to do this, but there seems to be not much problem with the mathematics.
A quick search in google scholar brought up only one page mentioning this kind of ensemble, a doctoral thesis about molecular simulation based around it. Does this mean that its possible to formulate it but not used very much?
A similar question could be posed about the $\mu$PE ensemble, I haven't found a single publication referring to it.