Exponential distributions of collective flow-event properties in viscous liquid dynamics.

We study the statistics of flow events in the inherent dynamics in supercooled two- and three-dimensional binary Lennard-Jones liquids. Distributions of changes of the collective quantities energy, pressure, and shear stress become exponential at low temperatures, as does that of the event "size" S identical with summation operator[under ][over ]d_{i};{2}. We show how the S distribution controls the others, while itself following from exponential tails in the distributions of (1) single particle displacements d, involving a Lindemann-like length d_{L} and (2) the number of active particles (with d>d_{L}).