Regularity and reversibility of cascading systems

The cascading of self-organized systems such as word processor line wraps or sandpile avalanches proceeds through complex dynamics maintaining the average balance through the gradual buildup and sudden release of stress through avalanches. Using simple algebraic arguments, we argue that the distribution of time differences between successive avalanches depends crucially on the reversibility of the system. For instance, in reversible systems avalanches never occur one immediately after the other, while in irreversible systems, successive avalanches are less anticorrelated. These arguments are confirmed by line-wrap and sandpile simulations of both reversible and irreversible systems.