Incorrect explanation of why states of matter are discrete There was a question on one of reddit's science communities where what the asker wanted to know is why states of matter are discrete and not a continuous spectrum.
The top answer was: "At the atomic level, the temperature of a substance is a measure of how energetic it's particles are. The higher the temperature, the higher the average kinetic energy of the atoms or molecules that make up that substance. For most substances, these particles attract one another with a strength governed by the various attractive forces at play, such as electric forces, van der Waals (sp?) forces, and chemical bonds. At low temperatures (and high pressures) the particles don't have enough energy to break these bonds, and the substance is solid. At medium temperatures some but not all of these attractive forces can be overcome, and at high temperatures the particles become completely separated and exist as a gas.
So why are there no in-between states? Because these bonds are binary; either they exist or they don't. Either the temperature is high enough to break the bonds, or it isn't. There is a very clear threshold above which the bonds are broken, and below which they remain intact. This translates into a clear division between states of matter.
Interestingly, because temperature is an average measurement, it's possible (and indeed quite likely) for individual particles to have a much higher or lower kinetic energy than that average and break or form bonds independently of the rest of the substance. This is how water can evaporate without boiling, for instance. It's also possible for particles in a solid substance to gain enough energy to sublimate directly into a gas."
A reply to this said that this is incorrect. And gave a statistical mechanics explanation which I don't have the background to understand.
Could someone explain in layman's terms why this answer is incorrect?
The source, for reference is: https://www.reddit.com/r/askscience/comments/pj9dit/why_is_there_discrete_states_of_matter_as_opposed/
 A: Please provide a reference to information you refer to. The thread is here.
The top answer is somewhat misleading because it explains the discreteness of phases through reference to individual molecules and individual bonds:

At low temperatures (and high pressures) the particles don't have enough energy to break these bonds, and the substance is solid.


So why are there no in-between states? Because these bonds are binary; either they exist or they don't.

The response correctly objects:

The key takeaway here is that phase transitions are a statistical effect. They cannot be understood just by looking at the molecules under a microscope: they are emergent phenomena. They only arise in systems with large numbers of particles.

It takes a large number of molecules for us to accurately gauge whether molecules in the bulk tend to easily slide past each other (liquid) or tend to be locked in place (solid). It takes a large number of molecules to gauge whether the surface tension is positive (condensed matter) or not (gas).
Quantitatively, we're interested in whichever phase has the lowest so-called Gibbs free energy, which governs the stable equilibrium state in familiar environments described by temperature and pressure. One phase can't "sort of" have a lower Gibbs free energy, which might result in a continuous transition between solid and liquid or liquid and gas; the energy is either lower or it isn't. Since the Gibbs free energy depends on the internal energy, temperature, entropy, pressure and volume, the sharp transition is thus connected to macrostate information, which is any information that doesn't average out to zero, given a very large collection of molecules. (An example of a macrostate parameter is pressure, which corresponds to the average rate at which the molecules strike a container wall. A contrasting example is the speed of individual molecules, which averages to zero relative to the frame of the bulk motion.)
Individual molecules and bonds can't reliably provide state information because fluctuations may act to make a specific molecule strongly or minimally energetic. (In a solid, an active molecule may jump out of place, leaving a thermal vacancy; this doesn't mean that molecule or the material in total is a gas. In a gas, a nonactive molecule may be essentially at rest relative to the system center of mass; this doesn't that molecule or the material has condensed or is a solid.)
A: 
So why are there no in-between states?

Because, strictly speaking, there are. At $0^{\circ}$C the same system can be in a state of ice, water, or any mix of ice and water. When you heat ice, the system goes through all these states. The effects of superheating and supercooling can further complicate the picture: the thermodynamics of nucleation depends on the balance of the bulk and the surface free energy of a nucleus.
A: One important aspect that I think other answers did not mention is that of thermal equilibrium. Usually, when one draws a phase diagram of a system, that diagram is for states in thermal equilibrium. In other words, it is assumed that thermal fluctuations, which are the effects that can happen microscopically when one specific atom or molecule has more energy than the average of the group, are negligible. That is usually a good approximation if you wait your system equilibrate long enough, but might not necessarily always be the case.
