L\'evy noise drives an exponential acceleration in transition rates within metastable systems

Abstract

L\'evy noise influences diverse non-equilibrium systems across scales, including quantum devices, active biological matter, and financial markets. While such noise is pervasive, its overall impact on activated transitions between metastable states remains unclear, despite prior studies of specific noise forms and scaling limits. In this work, we introduce a unified framework for L\'evy noise defined by its finite intensity and independent stationary increments. By identifying the most probable transition paths as minimizers of a stochastic action functional, we derive analytical scaling laws for escape rates under weak noise, thereby extending the classical Arrhenius law. Our results demonstrate that L\'evy noise universally enhances escape efficiency by reducing the effective potential barrier compared to Gaussian noise with equivalent intensity. Strikingly, even vanishingly weak L\'evy noise can exponentially increase escape rates across a broad range of amplitude distributions. This phenomenon arises from discontinuous most probable transition paths, where escape occurs via finite jumps. We validate these paths through the cumulant-generating function, a path integral representation, the mean first passage time and numerical simulations. Our findings reveal fundamental distinctions in escape dynamics under thermal and athermal fluctuations, suggesting new strategies to optimize switching processes in metastable systems through engineering noise properties.