REGULARITY AND REVERSIBILITY OF CASCADING SYSTEMS

The cascading of self-organized systems such as word professor line wr aps or sandpile avalanches proceeds through complex dynamics maintaini ng the average balance through the gradual buildup and sudden release of stress through avalanches. Using simple algebraic arguments, we arg ue that the distribution of time differences between successive avalan ches depends crucially on the reversibility of the system. For instanc e, in reversible systems avalanches never occur one immediately after the other, while in irreversible systems, successive avalanches are le ss anticorrelated. These arguments are confirmed by line-wrap and sand pile simulations of both reversible and irreversible systems.