Noise-Assisted Metastability: From Lévy Flights to Memristors, Quantum Escape, and Josephson-Based Axion Searches

Many-body and complex systems, both classical and quantum, often exhibit slow, nonlinear relaxation toward stationary states due to the presence of metastable configurations and environmental fluctuations. Nonlinear relaxation in a wide variety of natural systems proceeds through metastable states, which arise in condensed-matter physics as well as in fields ranging from cosmology and biology to high-energy physics. Moreover, noise-induced phenomena play a central role in shaping the dynamics of such systems far from equilibrium. This review develops a unifying perspective centered on noise-assisted stabilization and the statistical properties of metastable dynamics. We first discuss escape processes driven by Lévy flights in smooth metastable potentials, emphasizing the emergence of nonmonotonic residence-time behavior. We then connect these concepts to stochastic resistive switching in memristive devices, where noise-induced effects can enhance stability and reproducibility. We further examine driven dissipative quantum bistability, showing how the interplay between external driving and system environment coupling reshapes escape pathways and lifetimes. Finally, we outline how switching-time statistics in currentbiased Josephson junctions can provide an experimentally accessible strategy for axion detection, based on an axion-induced resonant-activation signature.