Time Directed Avalanches in Invasion Models

We define forward and backward time-directed avalanches for a broad class of self-organized critical models including invasion percolation, interface depinning, and a simple model of evolution. Although the geometrical properties of the avalanches do not change under time reversal, their stationary state statistical distribution does. The overall distribution of forward avalanches $P\left(s\right)\mathrm{}\sim s^{-2\mathrm{}}$ is superuniversal in this class of models. The power-law exponent $\pi$ for the distribution of distances between subsequent active sites is derived from the properties of backward avalanches.