system
Given the following post, respond as if you're commenting on Reddit:
human
Why are there states of matter (like solid, liquid, etc) instead of just smooth gradient from solid to gas?
gpt
There's a number of things to consider with this. The existence of discontinuous phase transitions can be predicted by characterising (or grouping) the states of matter by their symmetries. A gas has continuous translational symmetry while a solid crystal doesn't. So if you want to transition from a solid to a gas you will always have to encounter a discontinuous phase transition. On the other hand, both liquids and gases share the same symmetries (they're both ~~anisotropic fluids~~ aperiodic!!). Following the same reasoning, this would tell us that you can go from a liquid to a gas without undergoing a discontinuous phase transitions. This is achievable by transitioning from a liquid to a gas via a supercritical fluid - such a transition is continuous (or smooth as you put it).

This is why some people say glasses or plastics are super cooled liquids. Both liquids and glasses are anisotropic and so share symmetries. So you can undergo a smooth phase transition between them (the glass transition).