Follow up to
Suppose you have a piston with some air in it and you perform a slow, reversible expansion. The air in the piston must be in an equilibrium state the entire time.
Now suppose you do the expansion quickly. During the expansion, the air is not in an equilibrium state. My question is: should it have well-defined state variables? Should the pressure be well-defined, for example?
Presumably there is air moving around in bulk and a pressure gauge would give different readings depending on where you put it. Similarly, there is a mean kinetic energy of the molecules that might be used to define $T$, but there is no $\beta$ exponential factor because the kinetic energies of the molecules will not follow a simple, single-parameter distribution. This would indicate that concepts like pressure and temperature are not well-defined when out of equilibrium.
Is that right, and is it always the case? Can I have a process where I know what the pressure and temperature are the entire time, but the system is not in equilibrium?