Generalization of barrier crossing rate for coloured non Gaussian noise driven open systems

We have calculated the escape rate from a metastable of an open system driven by coloured non Gaussian and Gaussian thermal noise sources using the Fokker-Planck description of the stochastic process. We find that (i) the barrier crossing rate has a non-monotonic behaviour with the maximum as a function of the parameter of non-Gaussianity of the noise source; (ii) the crossing rate decreases rapidly for non Gaussian (NG) noise compared to Gaussian (G) with increasing noise correlation time; (iii) the crossing rate for NG noise reaches the limiting value before G noise. To check the validity of our approximate theoretical result we compared it with the numerical simulations and found a good agreement. Finally, we have checked that our general expression reduces to the standard Kramers' formula at an appropriate limit.