If you push a pile of sand very lightly, it will respond elastically, but if you push beyond an extremely low threshold, it will begin to flow. But the system that it flows into will be qualitatively similar to the state it was just in. We are studying that marginal transition in low dimensional systems (2D and 3D) using multiple approaches.
One way is to ask what is required to change states in a jammed solid (is it just a contact change, or something more?). Also, how are these state changes related to reversibility?