Noise Enhanced Stability in Fluctuating Metastable States

TL;DR

This paper derives exact equations for the lifetime of metastable states in fluctuating potentials, revealing noise-enhanced stability where noise increases the state’s lifetime, with implications for understanding stochastic systems.

Contribution

It provides a general analytical framework for the nonlinear relaxation time in systems with randomly switching potentials, highlighting the noise-enhanced stability phenomenon.

Findings

Noise can increase the lifetime of metastable states.

Maximum lifetime occurs at specific fluctuation rates.

Exact solutions valid for arbitrary noise intensities.

Abstract

We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: the average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise. We obtain the parameter region of the fluctuating potential where the effect can be observed. The system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential.