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" $S\equiv\sum {d_i}^2$. 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 $d>d_L$).