Exponential increase of transition rates in metastable systems driven by non-Gaussian noise

Abstract

Non-Gaussian noise influences many complex out-of-equilibrium systems on a wide range of scales such as quantum devices, active and living matter, and financial markets. Despite the ubiquitous nature of non-Gaussian noise, its effect on activated transitions between metastable states has so far not been understood in generality, notwithstanding prior work focusing on specific noise types and scaling regimes. Here, we present a unified framework for a general class of non-Gaussian noise, which we take as any finite-intensity noise with independent and stationary increments. Our framework identifies optimal escape paths as minima of a stochastic action, which enables us to derive analytical results for the dominant scaling of the escape rates in the weak-noise regime generalizing the conventional Arrhenius law. We show that non-Gaussian noise always induces a more efficient escape, by reducing the effective potential barrier compared to the Gaussian case with the same noise intensity. Surprisingly, for a broad class of amplitude distributions even noise of infinitesimally small intensity can induce an exponentially larger escape rate. As the underlying reason we identify the appearance of discontinuous minimal action paths, for which escape from the metastable state involves a finite jump. We confirm the existence of such paths by calculating the prefactor of the escape rate, as well as by numerical simulations. Our results highlight fundamental differences in the escape behaviour of systems subject to thermal and non-thermal fluctuations, which can be tuned to optimize switching behaviour in metastable systems.