Generalization of escape rate from a metastable state driven by external cross-correlated noise processes

TL;DR

This paper generalizes the escape rate from a metastable state considering external Ornstein-Uhlenbeck correlated noise, deriving a formula that accounts for noise correlation effects and validating it with simulations.

Contribution

It introduces a generalized escape rate formula for metastable states driven by correlated Gaussian noise, extending previous models to include external noise correlations.

Findings

Increased external noise correlation enhances escape rate.

Derived a Fokker-Planck-based expression matching simulations.

External noise correlation influences escape dynamics significantly.

Abstract

We propose generalization of escape rate from a metastable state for externally driven correlated noise processes in one dimension. In addition to the internal non-Markovian thermal fluctuations, the external correlated noise processes we consider are Gaussian, stationary in nature and are of Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective noise processes with finite memory we derive the generalized escape rate from a metastable state in the moderate to large damping limit and investigate the effect of degree of correlation on the resulting rate. Comparison of the theoretical expression with numerical simulation gives a satisfactory agreement and shows that by increasing the degree of external noise correlation one can enhance the escape rate through the dressed effective noise strength.