When is Grand Potential minimized?

1. May 13, 2012

5LAY3R95

1. The problem statement, all variables and given/known data

Is Grand Potential minimized in a process at constant volume, temperature and potential?

2. Relevant equations

Ω = A − ΣμN = −PV
Ω(V,T,μ) = −SdT − PdV − ΣNdμ

3. The attempt at a solution

As seen in the cases of U, H, A and G, I guess that when the differentiated variables used to express their infinitesimal changes are kept constant, each potential tends to a minimum.

Thus, in analogy, I guess that Ω tends to a minimum when temperature, volume and potential are constant. So ΔΩ in an spontaneous process like that is negative.

However the thermodynamic potential associated to G − ΣμN is constant = 0
So, I guess that the analogy is wrong?