Why is boiling a non-equilibrium process? Boiling is a non-equilibrium process. Which equilibrium (mechanical, chemical and thermal) are not maintained during boiling and why?
 A: There is a very basic answer to this question which I'll attempt to explain.
If you consider a system and its environment together as an isolated system in its own right, with the sum total energy being fixed (conservation of energy), then equilibrium for the system is defined as the situation where the probability measure over microstates does not change over time (canonical ensemble).
In boiling, this is clearly not the case; if you fix the total energy of the system and environment, eventually the environment will 'run out' of energy to boil the water, and boiling will cease. This is clearly not an unchanging distribution over microstates.
At this point you might ask if equilibrium is at all possible. To which the answer would be: Equilibrium is an idealized situation and in real life no system is ever in equilibrium. However, we can in a certain sense quantify how 'far away' a system is from equilibrium. A system away from equilibrium can still strongly approximate local equilibrium; if you zoom in on your boiling kettle and look at, say, a 1 micrometer square cube, it would be close to equilibrium.
A: I think the question, as is, does not have a single answer. It depends what you mean by boiling, and exactly which system you have in mind. Note that thermal equilibrium will always hold, as boiling is a first order phase transition with a latent heat. 


*

*If you have in mind boiling water over a stove in open air, i.e. you're heating the water up, then you are right that you are not in (thermodynamics) equilibrium. Because in thermodynamics equilibrium, the chemical potentials of the different substances must be equal. In that case this means that $\mu_\text{liquid water}$ must equal $\mu_\text{gaseous water}$. But clearly this does not hold, because water in liquid form tends to become water in gaseous form.

*If you have in mind a closed or isolated container in which liquid and gasesous phases of say water coexist, then you can have thermodynamics equilibrium when the water is boiling. The chemical potentials of the various forms of water will match, so to any bubble of vapor will correspond a same amount of water vapor condensation, in average.


In all cases, mechanical equilibrium does not hold, because this would require that the net force on every single region of the system vanishes. The formation of a bubble does create a force on the liquid around it, so clearly, boiling does not preserve mechanical equilibrium.
A: Boiling is close to being in thermodynamic equilibrium.  But the bubbles are rising buoyantly (and accelerating), so, to some extent this is non-equilibrium.  Also, the bubbles are churning the water so that the water is deforming; the viscous dissipation associated with this is also an irreversible non-equilibrium effect.  Finally, there have to be finite temperature gradients in the water, since heat transfer is taking place from the source of the heat; this too is a non-equilibrium effect.  But, as I said, to a good approximation, the situation is close to being at thermodynamic equilibrium with regard to the relationship between the pressure and temperature of the bubbles, and that of the liquid water in close proximity to the bubbles.
