Connecting the random organization transition and jamming within a unifying model system.

While the random organization transition describes the change from reversible to irreversible dynamics in a nonequilibrium system, the athermal jamming transition at zero shear rate occurs when particles can no longer avoid overlaps. Despite the obvious differences between these two transitions, we show that they both occur within the same model packing problem. In this unifying model system the particles are first randomly distributed and then displaced in each step if they overlap. For random displacements we obtain a random organization transition, while jamming occurs in the case of deterministic shifts. We also analyze the critical behavior of random organization. Our results show that random organization and jamming are opposite limits of random sphere packings, and we expect that various equilibrium and nonequilibrium transitions can be formulated as related intermediate packing problems.