Mapping of a deterministic dynamics with quenched variables into a stochastic problem with cognitive memory

Irreversible dynamics in media with quenched disorder seems to be the essential mechanism for a variety of phenomena like fracture propagation or displacement of immiscible fluids in disordered porous media. This problem does not seem to be treatable along the standard theoretical schemes. Recently a new approach has been introduced that allows mapping of a deterministic dynamics with quenched disorder like that of Invasion Percolation into a stochastic dynamics with memory. This memory consists essentially in a cognitive process that modifies the probability distribution of quenched variables conditionally to all previous events. This approach, together with the FST and the corresponding analysis of the scale invariant dynamics, provides a new framework to understand the self organization and to compute the critical exponents of problems like Invasion Percolation and Bak and Sneppen.