Isomolar semigrand ensemble

The fugacity fraction is a convenient quantity because it is bounded between zero and unity, and it has a qualitative correspondence with the mole fraction. The set of fugacity fractions are not independent, as they must sum to unity. Instead the complete set of independent chemical variables is specified by m — 1 fugacity fractions together with the sum Yj=i fj In terms of fugacity fractions the isomolar semigrand ensemble of Eq. (2.5) is expressed... 

It is necessary to know the form of the partition functions to construct transition probabilities that properly sample the ensemble. For instructional purposes we record here the (semiclassical) partition functions that correspond to the osmotic and isomolar semigrand ensembles described above. In both ensembles one must average over moles of the Legendre-transformed species. Thus the osmotic semigrand ensemble partition function is... 

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