Free energy minimization and partition functions in thermodynamics

[secret2]

I am quite confused by some aspects of thermodynamics. First of all, I just wonder, when the textbook says that "when the constraints are temperature, volume and particle number, minimise F for equilibrium" (and similar statements for G and H), does it mean that the temperature, volume and particle number of the sub-system (i.e. excluding the reservoir) is fixed?

And also, if Z, the partition function, is given, how should I proceed to find the equation of state?

Thank you.

 

[shyboy]

Because
$$dF \leq -SdT -PdV + \mu dN$$
then at fixed volume , temperature, and particle number, the free energy can only decrease, if we are at non-equilibrium. Thus temperature, volume, and particle number called "natural" arguments for the free energy.

If you know a partition function, you can calculate free energy. After that you can find pressure, enthropy, and thermodynamic potential using the thermodynamic identities