Most Probable Transitions from Metastable to Oscillatory Regimes in a Carbon Cycle System

Wei Wei, Jianyu Hu, Jianyu Chen, Jinqiao Duan

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

Both sources align on the SDE, quasi-potential and gMAM method, the ν≈0.2 switch in transition pattern, and the decrease of arrival c from >150 to ~50 μmol·kg−1 for cx=62; see the abstract and Sec. 4 with Figs. 3–6 of the paper . The candidate’s procedure (sampling endpoints on the limit cycle, minimizing V((c*,w*),D)) mirrors the paper’s equation (3.5) and narrative . Minor issues: the paper’s LDP display (3.2) has the wrong limit direction and scaling relative to the SDE (Eqs. 2.5–2.6 vs 3.1–3.5) , and the candidate mis-cites the arrival-value plot (it is Fig. 5b, not 4b) . These do not alter the computed minimizers or the qualitative conclusions.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper and the candidate solution both apply standard large-deviation machinery and gMAM to a timely carbon-cycle model, reaching consistent and interpretable conclusions. The numerics convincingly demonstrate a switch in the most probable landing sector near ν≈0.2 and a monotone decrease in arrival c. Minor theoretical typos (LDP scaling/limit) and some missing algorithmic details are easily correctable and do not undermine the results.