x ∗ n 30 25 20 15 10 5 0 14 12 10 8 6 4 2 0 t ∗ = 0 t ∗ = 10 t ∗ = 10 0 FIG. 3: Diffusion profile for the molecules moving from the path integral region to the coarse grained one and for molecules moving in the opposite direction, for the system at temperature T $_{1}$. The picture shows that no barriers, due to possible artifacts of the algorithm, hinter the diffusion process. 11