point at (-0.8,0.6)). This example is obviously very simple and serves no other purpose than being a benchmark: the application of our sampling procedure to more interesting examples will be reported elsewhere. To avoid confusions, before presenting our results for (\[eq:langevin\]) let us note that this system is an equilibrium one, with equilibrium density $\varrho(\xx,\vv)= Z^{-1} \exp(-\beta H(\xx,\vv))$ where $H(\xx,\vv) =
\frac12 |\vv|^2 + V(\xx)$ is the Hamiltonian and $Z =
\int_{\RR^2\times\RR^2}\exp(-\beta H(\xx,\vv))d\xx d\vv$ the partition function. We are, however, primarily interested in computing the reaction rates between the reactant state $A$ and the product state $B$ shown in Fig. \[fig:potMull\], which we will achieve by twisting the dynamics as explained before to focus on trajectories assigned to $A$. In so doing, we automatically put the system out of equilibrium since $A$ becomes a source and $B$ a sink (and $\varrho_A(\xx,\vv)
\not = \varrho(\xx,\vv)$). This is why we need the nonequilibrium formalism developed above to compute reaction rates even in the case of an equilibrium system such as (\[eq:langevin\]).

Shown in Fig. \[fig:potMull\] are the 36 cells that we used in our calculations. These cells were defined as $$\label{eq:Bkx}
  \begin{aligned}
    B_{\alpha}=
    \{(\xx,\vv) \in \RR^2\times\RR^2 \; : \;
    |\xx - &\xx_{\alpha}|<|\xx-\xx_{\beta}| 