Gibbs potential and phase transitions I'm studying phase transitions on Callen's book Thermodynamics and an Introduction to Thermostatistics (chapter 9, section 9.1) but I had some problems while trying to understand the role of the presence of multiple minima in the Gibbs free energy.
In the first part of the chapter, Callen makes this example: imagine a vessel of water vapor at a pressure of 1 atm and at a temperature somewhat above 373.15 K, that is slightly above the boiling point. Now consider a small subsystem consisting of a spherical region containing one milligram of water. The radius of this region can change depending on the density of vapor.
Callen arguments that this region is in effective contact with a thermal reservoir and a pressure reservoir. Therefore, the equilibrium of this small subsystem is determined by the minimization of the Gibbs potential G(T,P,N) of the subsystem itself.
My first question is this: How can we minimize G(T,P,N) when T and P are constant (the subsystem is in contact with a thermal and pressure reservoir) and N is constant too (the subsystem contains exactly 1 mg of water)?
After that, Callen continues: "The two independent variables which are determined by equilibrium conditions are the energy U and the volume V of the subsystem".
So, my second question (following directly from the first one) is this: The function G(T,P,N) apparently has no independent variables left! What independent variables are we talking about, then?
Evidently, I'm misunderstanding something important. Can you help me, please? Thank you in advance!
Edit: Maybe I forgot some important information needed to understand my question. I tried to clarify some points in the comments to the answers. However, thank you very much for your answers!
 A: Remember, the Gibbs free energy is related to the amount of reversible work that may be performed at constant temperature, T, and pressure, p.  For thermodynamic equilibrium, at a specified p and T, the Gibbs free energy is at a minimum.  The chemical potential is central to such considerations.  Restated, this potential is useful for calculating equilibrium chemical concentrations.
1) The Gibbs free energy has natural variables of p and T.  At constant p and T, the Gibbs free energy is depending on the extent of reaction, xi, to reach thermal equilibrium.  To minimize G, you differentiate with respect to xi.
2) G(p,T) = U + pV - TS. So, the internal energy and volume are determined by the equilibrium conditions.
A: This is a very common misunderstanding regarding the stationarity of any of the thermodynamic potentials be it $S$ or $U$ or $G$, etc. For example, in your question the function $G(T, p, x_1,x_2,..$, a general Gibbs function whose independent variables are temperature, pressure, and anything else that may affect the system $x_1, x_2,...$ (e.g., chemical concentration, magnetic field, etc.,) is a function of these variables and the energy balance $dG = -SdT + Vdp +y_1dx_1 + y_2dx_2+..$ is true irrespective of whether the system is in equilibrium or not. Of course if it is in contact with a constant temperature heat source and a constant pressure work source so that during the energy exchange the system's temperature and pressure are constant then you can also write that $dG = y_1dx_1 + y_2dx_2+..$.
Again, the function $G$ is meaningful whether the system is or is not in equilibrium with its environment. The stationarity of $G$ means that if you have  system that is not in equilibrium now but it is also in contact with a constant temperature heat source and a constant pressure work source then it will evolve towards equilibrium by the other variables $x_1, x_2,..$ that minimize $G$ when it will be in equilibrium with its environment.
The $G(T,p,N)$ function you are referring to is for a given phase, say $G_1(T_1,p_1,N_1)$ so to achieve phase equilibrium between this and another phase, say $G_2(T_2,p_2,N_2)$ only the quantity $N_1+N_2$ is constant and $N_1$, thus $N_2$ is variable so that $G_1+G_2$ is minimized.
A: You are right in saying that $N$ is fixed since we impose that the spherical region of space that we are considering contains exactly $1$ mg of water.
If this was the usual discussion about equilibrium thermodynamics, you would be right: since the subsystem is in contact with a reservoir, $T$ and $P$ (and hence $V$) are constant, too.
But here Callen is explicitly considering fluctuations, so this line of reasoning is not going to work. Let's see why (I will talk about temperature but the same is of course valid for pressure).
When we say that $T$ has a certain value we mean that it takes that value on average: in reality, there will always be fluctuations, i.e. if you were to measure $T$ accurately enough you would see something like this (average value in red):

These fluctuations are completely random from a macroscopic point of view, since they come from the microscopic dynamics of the system, which is not under our control. Moreover, the smaller the system, the larger the fluctuations (it can be shown that they are proportional to $1/\sqrt{N}$).
Callen talks about fluctuations in volume, but the concept is the same: $T$,$P$, and hence $V$ are all fluctuating; only $N$ is not since we fixed it by definition.
So, when we say that the system is in a in a free energy minimum, corresponding to a certain value of the three parameters $(T,N,P)$, we must understand that these values are actually fluctuating, and that the system is actually "wiggling around" in the minimum, continuously going to states $(T',P',N) \neq (T,N,P)$. 
But every time it gets away from the minimum, the restoring mechanism coming from the condition that $G$ must be minimized comes into play, taking it back there.
