Gibbs Free Energy and the Grand Potential

[Useful nucleus]

Gibbs Free Energy is the appropriate potential when there is both heat exchange and mechanical work (G=E-TS+PV). On the other hand the grand potential is appropriate when there is heat exchange and chemical work (g=E-TS-μN).
Is there any issue in defining a potential of the form (E-TS-μN+PV) such that it is conserved in some ensemble? If there is no problem, is there a consensus on a name for such potential and its corresponding ensemble?

 

[DrDu]

The problem is probably that the corresponding potential vanishes identically as G=mu N and g=-PV. You need the potential to depend on at least one extensive variable. If not, you can no longer specify the amount of substance you are talking about.