Multiplicative cross-correlated noise induced escape rate from a metastable state

TL;DR

This paper develops an analytical and numerical framework to analyze how cross-correlated multiplicative noise influences the escape rate from a metastable state, revealing that increased correlation enhances the escape rate.

Contribution

It introduces a novel analytical approach for calculating escape rates under cross-correlated multiplicative noise in nonequilibrium systems, validated by numerical simulations.

Findings

Rate increases with higher correlation degree of external noise

Analytical results agree with numerical simulations for constant dissipation

External cross-correlated noise can significantly enhance escape rates

Abstract

We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers' theory for activated rate processes in a nonequilibrium open system (one-dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same. By employing numerical simulation in the presence of external cross-correlated additive and multiplicative noises we check the validity of our analytical formalism for constant dissipation, which shows a satisfactory agreement between both the approaches for the specific choice of noise processes. It is evident both from analytical development and the corresponding numerical simulation that the enhancement of rate is possible by increasing the degree of correlation of the external fluctuations.