  A central paradigm of non-equilibrium physics concerns the dynamics of
heterogeneity and disorder, impacting processes ranging from the behavior of
glasses to the emergent functionality of active matter. Understanding these
complex mesoscopic systems requires probing the microscopic trajectories
associated with irreversible processes, the role of fluctuations and entropy
growth, and the timescales on which non-equilibrium responses are ultimately
maintained. Approaches that illuminate these processes in model systems may
enable a more general understanding of other heterogeneous non-equilibrium
phenomena, and potentially define ultimate speed and energy cost limits for
information processing technologies. Here, we apply ultrafast single shot x-ray
photon correlation spectroscopy to resolve the non-equilibrium, heterogeneous,
and irreversible mesoscale dynamics during a light-induced phase transition.
This approach defines a new way of capturing the nucleation of the induced
phase, the formation of transient mesoscale defects at the boundaries of the
nuclei, and the eventual annihilation of these defects, even in systems with
complex polarization topologies. A non-equilibrium response spanning >10 orders
of magnitude in timescales is observed, with multistep behavior similar to the
plateaus observed in supercooled liquids and glasses. We show how the observed
time-dependent long-time correlations can be understood in terms of the
stochastic dynamics of domain walls, encoded in effective waiting-time
distributions with power-law tails. This work defines new possibilities for
probing the non-equilibrium and correlated dynamics of disordered and
heterogeneous media.
