Exploring the use of Transition Path Theory in building an oil spill prediction scheme

The paper explicitly states Proposition 1: compute the forward committor on the augmented chain with A+ = R ∪ ω and B+ = P, and the backward committor with A− = R and B− = P ∪ ω; it asserts that the standard TPT formulas then apply on the extended state space D̃ (with P̃, π̃) to isolate oil that last exited R, stays in D, and next hits P (before any escape to ω). This matches the model’s boundary choices and target ensemble. The paper gives a succinct justification (and Figure 1’s interpretation), but no formal proof, whereas the model supplies a clean pathwise proof and a necessity argument for including ω in A+ and B−. The two are consistent: the model formalizes the paper’s proposition and shows that π̃(i) q̃−(i) q̃+(i) indeed equals the occupancy of reactive points under those choices (using conditional independence of past and future given Xn = i). Thus, both are correct; the model provides the missing detailed proof. Key statements: Proposition 1 and the augmented chain P̃ (11) , standard TPT formulas including πABi = q−i πi q+i , and the intended definition of reactive trajectories that ‘flow last from R and next go to P while staying in D’ (Figure 1 caption) .