  "\textit{The noise is the signal}"[R. Landauer, Nature \textbf{392}, 658
(1998)] emphasizes the rich information content encoded in fluctuations. This
paper assesses the dynamical role of fluctuations of a quantum system driven
far from equilibrium, with laser-aligned molecules as a physical realization.
Time evolutions of the expectation value and the uncertainty of a standard
observable are computed quantum mechanically and classically. We demonstrate
the intricate dynamics of the uncertainty that are strikingly independent of
those of the expectation value, and their exceptional sensitivity to quantum
properties of the system. In general, detecting the time evolution of the
fluctuations of a given observable provides information on the dynamics of
correlations in a quantum system.
