Fig. 3

Illustrations of the simple Gaussian mixture approximation and the modified Gaussian mixture approximation to the accurate energy landscape in the regime of slow switching rates. a The solution of CME which we take as the accurate energy landscape. b Illustration of the simple Gaussian mixture approximation. c Illustration of the modified Gaussian mixture approximation. d, e, f The relative errors of two approximation methods on the open layer, closed layer and global energy landscape. Dashed lines correspond to the simple Gaussian mixture approximation and solid lines correspond to the modified approximation. We use the KL divergence (i.e. Kullback-Leibler divergence) to measure the difference between two approximations and the accurate solution of CME. To make the KL divergence well defined, we assume that the minimum value of the distributions in the truncated domain is 10⁻¹⁶ (i.e. replace the values which are less than 10⁻¹⁶ with 10⁻¹⁶). From the quantitative comparisons, we find that the modified approximation is superior than the simple approximation since more detailed information are encoded. Parameter values are the same with those in Fig. 2