A Dynamical Mechanism for Irreversibility in Cyclically Driven Amorphous Solids

Amorphous solids subjected to athermal quasistatic oscillatory shear undergo a transition from periodic reversible dynamics to irreversible diffusive dynamics at yielding. How irreversibility arises in such deterministic, dissipative dynamics remains unclear. Here we show that trajectories remain locally stable, with perturbations decaying rather than growing even in the irreversible regime, ruling out the sustained exponential sensitivity to initial conditions associated with chaotic dynamics. Rather than diverging continuously, nearby trajectories initially remain close before eventually separating through rare branching events, after which their separation grows diffusively. A mean-field soft-spot model reproduces the same branching statistics and reveals their microscopic origin. We find that branching originates from competition between nearly-degenerate plastic instabilities, in which a small perturbation changes which instability activates first and thereby alters the subsequent sequence of plastic events. These results identify instability-selection-induced branching as a dynamical mechanism for irreversibility in cyclically driven amorphous solids.