Heterogeneous activation in 2D colloidal glass-forming liquids classified by machine learning*

The trajectories of particles in colloidal glass-forming liquids are often characterized by long periods of ``in-cage'' fluctuations and rapid ``cage-breaking'' rearrangements. We study the rate of such rearrangements and its connection with local cage structures in a 2D binary mixture of poly(N-isopropyl acrylamide) spheres. We use the hopping function, $P_\mathrm{hop}(t)$, to identify rearrangements within particle trajectories. Then we obtain distributions of the residence time $t_R$ between consecutive rearrangements. The mean residence time $\bar{t}_R(S)$ is found to correlate with the local configurations for the rearranging particles, characterized by 70 radial structural features and softness $S$ [PRL 114, 108001 (2015)], which ranks the structural similarities with respect to rearranging particles. Furthermore, $\bar{t}_R(S)$ for particles with similar softness decays monotonically with increasing softness, indicating correlation between rearrangement rates and softness $S$. Finally we find that the conditional and full probability distribution functions, $P(t_R|S)$ and $P(t_R)$, are well explained by a thermal activation model.