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: 
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.
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> How exactly did Dirac incorporate SR into his wave equation?
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Relativity treats space and time on equal footing. Lorentz transformations ("boosts") "mix" space and time more or less analogously to the way a 3-dimensional rotations "mixes" the usual $(x,y,z)$ coordinates of space.

The Schrödinger equation describes non-relativistic quantum mechanical systems well, but is second-order in spatial derivatives and first-order in the temporal derivatives. In other words, space and time are not on equal footing.

Dirac, being a formal theorist, looked for an equation that would reproduce predictions (e.g., the energy levels of Hydrogen in the limit of slowly moving electrons) of the non-relativistic theory while treating space and time on equal footing. The equation which he discovered and now bears his name is a first-order differential equation in space and time. This "equal treatment of space and time" is the sense in which the Dirac equation incorporates special relativity.