The use of a phase transition to describe reality pops up in this paper by George Ellis and Tony Rothman: “Time and Spacetime: The Crystallizing Block Universe.”
I had previously read Ellis’ contribution to the FQXi contest on time: “On the Flow of Time”. In that essay, Ellis criticized the notion of picturing the universe as an unchanging four-dimensional space-time block, and proposed a model of an “Evolving Block Universe”, which includes the indispensable notion of time flow. In this new paper, Ellis and Rothman fine-tune this idea.
They associate the flow of time with the transition from a quantum future to a classical past: this transition is marked by the time-irreversible process of quantum state-vector reduction (measurement). They note, however, that phenomena displayed in certain quantum set-ups (delayed choice and quantum eraser schemas) show that the transition process doesn’t take place uniformly. This non-uniform nature of the transition inspired the crystallization metaphor.
I like that Ellis takes quantum measurement seriously as a natural process (actualizing potentialities) and links this transition to the experienced flow of time.