Dispersion of the prehistory distribution for non-gradient systems

The most probable escape path can reveal the optimal fluctuation with overwhelming probability for vanishing noise during escape. However, it fails to offer information for the feature of the nearby paths, while the dispersion of the prehistory distribution does. For gradient systems, the dispersion can be obtained via a relaxation method which takes the advantage of the time reversibility of the fluctuation-dissipation relation. For non-gradient systems, due to the breaking of the time-reversal symmetry, the traditional relaxation method cannot be applied. In this paper, we investigate the dispersion of the exit phenomena in the Maier-Stein system for three sets of parameters. For the gradient case, the traditional relaxation method is extended to the 2D situation. For the non-gradient case, we propose a revised version of the relaxation method which relies on the computation of quasipotential. The results are compared with those of Monte Carlo simulation which shows the efficiency of the algorithms.