One-Way Hysteresis in the Depinning Transition

We identify a mechanism for a type of hysteresis which we predict to occur in a variety of depinning transitions. We show that the phenomenon of one-way hysteresis is generic to stress-overshoot models of the depinning transition, and we show how to calculate the size of the hysteresis gap exactly in a large class of models. Unlike thermodynamic phase transitions, the dynamic phase transition is still {\em continuous} despite the presence of hysteresis because the terms which produce the hysteresis are renormalization group irrelevant. We discuss the experimental and numerical signatures of one-way hysteresis, which includes microscopic nucleation.