Quasi-Static Loading and the Loss of Equilibrium: A Fold-Catastrophe Perspective

Classical systems subjected to slowly varying external conditions are commonly assumed to evolve through a continuous sequence of equilibrium states. Under this quasi-static approximation, stability is often interpreted as persistence of equilibrium under gradual loading. In this work, we argue that sudden dynamical transitions in slowly driven systems need not arise from growing instabilities or chaotic effects, but can instead result from the disappearance of admissible equilibrium configurations. When equilibrium solutions cease to exist as control parameters evolve, the system is forced into rapid motion and unavoidable energy release, even under arbitrarily slow driving. This structural perspective clarifies the origin of abrupt events in classical systems and highlights fundamental limits of quasi-static descriptions.