Other ensembles of systems and associated characteristic functions

Other ensembles of systems and associated characteristic functions 

In this chapter we have deseribed a canonieal ensemble. In fact, an ensemble is chosen according to the set of independent variables selected, i.e. volume, temperature and amount of matter of the canonical ensemble. For this ensemble, we defined a canonical partition function by relation [5.8]. 

Moreover, as seen in Chapter 1, each set of variables has a corresponding characteristic function, which is the thermodynamic potential. We saw that this is the Helmholtz free energy for variables linked to a eanonioal ensemble. Also note that this function is linked to the statistical description from the relation [5.42] and to the logarithm of the partition function of the corresponding ensemble. 

In the same way as we chose in Chapters 1 and 2 the characteristic function and a characteristic matrix for each set of independent variables Ep, we can link to this set an ensemble, as in section 5.2, snch that the relation between the characteristic function and the partition function linked to this ensemble, i.e. in the same form as in relation [5.42]. 

for example, if we choose the set of independent variables temperatnre, volnme and chemical potential, we show that the characteristic function is the prodnct -PF the corresponding ensemble is called the 

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