  We study the equilibration behavior following local quenches, using
frustrated quantum spin chains as an example of interacting closed quantum
systems. Specifically, we examine the statistics of the time series of the
Loschmidt echo, the trace distance of the time-evolved local density matrix to
its average state, and the local magnetization. Depending on the quench
parameters, the equilibration statistics of these quantities show features of
good or poor equilibration, indicated by Gaussian, exponential or bistable
distribution functions. These universal functions provide valuable tools to
characterize the various time-evolution responses and give insight into the
plethora of equilibration phenomena in complex quantum systems.
