Question: I'm a first timer here. In a normal liquid-vapor P-V biphasic curve at a temperature below critical temperature, we can compress a vapor at a constant temperature till it becomes saturated, or is just about to turn into a liquid. Any further compression would lead to the existence of the two phases together, as we know. Here we can see from the phase rule that we have just one degree of freedom. So just specifying the temperature will set the pressure and volume, just like what the Antoine equation gives. 

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A pre-question here is that once we come into the zone inside the bell curve of mutual phase existence, what does the volume in the X-axis specify? (Like volume of the gas or volume of the liquid)

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My main question is once it enters this zone where the temperature and pressure are set at a saturated value, what is the driving force for the conversion of the vapor to liquid. By this I mean, how can we ensure that two distinct desired compositions can be achieved if we perform the experiment two different times. Surely this isn't to be a transient process where the end result is always full saturated water.
I would really appreciate if someone could clear this for me. I have tried looking everywhere for an answer to this, and I did not find it here either. Pardon me if I didn't look enough here.

Answer: 
This answer is meant to add to [Luke's excellent concise answer](https://physics.stackexchange.com/a/335094/26076), so please read his answer first.

In quantum mechanics, only measurements have the statistical distributions, the "uncertainties" and all the things that are (validly) bothering you. As you point out, this makes notions of *measured* spacetime co-ordinates problematic. 

But the underlying theory that lets one calculate these statistical distributions can be Lorentz-invariant. 

It is not emphasized enough, particularly in many lay expositions, that much, if not most of quantum mechanics is *utterly deterministic*. This deterministic part is concerned with the description and calculation of the evolution of a system's quantum state. Aside from some more modern mathematical techniques and notations, this part of quantum mechanics probably wouldn't look very alien or physically unreasonable to even Laplace himself (whom we can take as a canonical thinker from the philosophy of determinism). This quantum state evolution takes place on an abstract spacetime manifold just like classical physics. When a quantum theory is said to be relativistic or Lorentz invariant, it is usually the deterministic quantum state space evolution that is being talked about. Note, in particular, that no measurement takes place in this part of the description, so there's no problem with a spacetime manifold parameterized by zero uncertainty spacetime co-ordinates.

We model *measurements* with special Hermitian operators and recipes for handling them called *observables*. Given a system's quantum state, these operators let us work out the statistical distributions of outcomes of the measurements we can make on a system with that quantum state. When people talk of quantum uncertainty, Heisenberg's principle and all the rest of it, they are speaking about the statistical distributions that come from these measurements. So, whilst Schrödinger's equation (the deterministic, unitarily evolving description) for the electron in a hydrogen atom is written in terms of zero uncertainty space and time co-ordinates (known as *parameters* to emphasize that they are not measurements), the outcome of a position *measurement* is uncertain and the position observable lets us calculate the statistical distribution of that outcome.
There is no full consensus about what relativistic means, but as a good start, we can take the criterion given by Tim Maudlin in his paper "Space-Time in the Quantum World":

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> [A] theory is compatible with Relativity if it can be formulated without ascribing to space-time any more of different intrinsic structure than the [...] relativistic metric.
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This directly implies that the laws must be invariant under Lorentz transformations, there is no preferred frame as such and nothing can propagate faster than light. This is a good notion since it does not need things like "speed of a photon" that are, as you pointed out, a bit problematic.