  Many molecular systems and physical phenomena are controlled by local
fluctuations and microscopic dynamical rearrangements of the constitutive
interacting units that are often difficult to detect. This is the case, for
example, of phase transitions, phase equilibria, nucleation events, and defect
propagation, to mention a few. A detailed comprehension of local atomic
environments and of their dynamic rearrangements is essential to understand
such phenomena, and also to draw structure-property relationships useful to
unveil how to control complex molecular systems. Considerable progresses in the
development of advanced high-dimensional structural descriptors (e.g., Smooth
Overlap of Atomic Position (SOAP), etc.) have certainly enhanced the
representation of atomic-scale simulations data. However, despite such efforts,
local dynamic environment rearrangements remain still difficult to elucidate.
Here, exploiting the structural-rich description of atomic environments of SOAP
and building on the concept of time-dependent local variations, we developed a
time-dependent SOAP-based descriptor, TimeSOAP (tSOAP), which essentially
tracks the time variations in the local SOAP environments surrounding each
molecule (i.e., each SOAP center) in complex molecular systems along ensemble
trajectories. We demonstrate how analysis of the time-series {tSOAP data and of
their time-derivatives allows detecting dynamics domains and tracking
instantaneous changes of local atomic arrangements (i.e., local fluctuations)
in a variety of molecular systems. The approach is simple and general, and we
expect will help to shed light on a variety of complex dynamical phenomena.
