States and transitions in a simple model of a grassy path with park benches along it. The model has surprisingly rich memory behaviors, including learning, forgetting, and a stabilizing effect of noise.

We typically think of memory as the stuff stored in hard drives or our brains, but memory effects abound in a wide range of materials. Rubber and rocks can remember the largest load that was applied to them, glasses may remember a temperature where they were aged, and shape-memory alloys can recall a programmed shape. One approach to building a broader understanding of memory formation in matter is to construct and study simple models where memories may be written, stored, and retrieved. This article shows how a model of worn grass between park benches can produce a peculiar memory behavior that has been observed in the motion of electrons in a special kind of conductor, and in the flow of solid grains in viscous liquids. As in the other systems, the “park bench model” can store multiple pieces of information in transient states, but it forgets all but the largest repeated excursion in the steady state. Our work provides an example of this kind of memory on a human scale, and demonstrates that neither criticality nor nonlinear diffusion are behind it.