Rattachai Pinchaipat is a crafty experimentalist (PhD student in Bristol) that I have had the pleasure to work with within a Bristol-Mainz collaboration aimed at demonstrating in experiments the existence of phase transitions in trajectory space for supercooled liquids. Our work is going to appear in Physical Review Letters. Here is the preprint.
In Mainz, preliminary simulations on hard spheres in trajectory space (by Matteo Campo) have sampled the tails of the probability distribution of time-integrated structural observables and predicted long non-gaussian tails (signature of a phase transition). In experiments, Rattachai managed to find an analogous signature via subsampling the trajectories of a rather large system.
The result demonstrates that the dynamical heterogeneities that characterise fragile glass forming liquids can be read as the coexistence, in trajectory space, of different long-lived (metastable) stationary states: some are structure-less, while others show the presence of extraordinary extended and long-lived motifs. Crucially, the phase transition between the two states is not accessible in current experiments, and could eventually never be accessible, if it is always buried in the tails of the probability distribution.
But this is another story… (actually, this story).