{"id":"6d38b2ba-e5db-4c02-9a60-ad04d81577e3","arxiv_id":"2507.10516","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Using a fitted stochastic model of daily SOI fluctuations, the authors compute entropy variations for 11 ENSO phase transitions and find none are extreme except possibly the 1999-2000 La Niña to 2002-2003 El Niño transition.","lead":"This paper applies stochastic thermodynamics to daily Southern Oscillation Index data to compute entropy changes during 11 El Niño/La Niña transitions. It finds that only one transition approaches the threshold of an 'extreme' entropic event, offering a new way to quantify ENSO phase changes.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fitted drift parameter b appears with opposite signs in Eq. (1) (+0.08) and the SM fit (−0.08), so every reported entropy variation may have been computed with the wrong drift; the classification of transition 4 as a 4σ event is not yet robust.","rationale":"The paper's central claim is that only transition 4 sits at the edge of being an extreme entropic event. That claim is a ratio of a model-derived ΔS to a model-derived σ, so it inherits every error in the model parameters. The unresolved b sign is the most load-bearing issue because it is internal and directly checkable; unlike general doubts about Markovianity or Gaussian noise, it does not depend on outside assumptions about the climate system. The reader's verdict already flags the b inconsistency in its rationale, but its formal weakest_assumption is the stationarity/truncation assumption; my concern is narrower and more decisive. I therefore recommend keeping the CONDITIONAL verdict: the paper should either correct the inconsistency and re-run the tables, or explicitly state which value of b was used, before the 4σ classification is accepted. A failure of the proposed check would not necessarily overturn the broad 'no extreme events' conclusion, but it would change the specific 'only nr 4 is near extreme' claim.","tokens_in":26755,"tokens_out":3603,"duration_ms":42027,"concrete_test":"Re-estimate b from the first Kramers-Moyal moment via Eq. (15) of the SM on the public daily SOI series; then recompute Tables II and III twice, once with b=+0.08 and once with b=−0.08, all other fitted parameters held fixed, and report which sign was used in the original calculations. If transition 4 no longer exceeds 4σ in Table II (or 3σ in Table III), or if a different transition crosses the threshold, the headline extreme-event claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Main-text Eq. (1) reports D1(ξ) = −aξ + b with b = 0.08 ± 0.01, while the SM section 'Computation of the Kramers-Moyal coefficients' reports the fit result b = −0.08 ± 0.04 from the same data. The sign of b enters the transformed dynamics (Eq. 7), the stationary density (Eq. 6), and every term of the forward/reverse propagators Ω_i^F/R in the SM, so the values of ΔS, ⟨ΔS⟩, and σ in Tables II and III are not reproducible as printed. If the published calculations used +0.08 where the fit gives −0.08, the drift in Eq. (7) is reversed, and the quantitative extreme-event classification is suspect. If −0.08 was used and the main text is a typo, the paper still does not say which value was actually used, so a reader cannot verify the headline claim. This is an internal inconsistency, not a question of modeling consensus: it can be settled by recomputation. The paper's IFT checks do not help, since forward and reverse probabilities are generated from the same model, so the fluctuation relation is satisfied by construction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper analyzes daily Southern Oscillation Index (SOI) data from 1991–2023 to study entropy production during 11 catalogued El Niño/La Niña transitions. The SOI series is decomposed into a deterministic 'protocol' Φ(t) obtained by multi-taper spectral analysis and a residual ξ(t), which is modeled as a stationary Markov process with a linear drift and a quadratic diffusion coefficient (Eq. 1). After a Lamperti transformation to additive noise and a saddle-point evaluation of the Onsager–Machlup path integral, the paper derives forward and reverse transition probabilities and computes the stochastic entropy variation ΔS for each transition, both along the full observed trajectory (Table II) and using only the endpoints (Table III). The paper reports that all transitions satisfy the integral fluctuation theorem and finds that only transition 4 (1999–2000 La Niña to 2002–2003 El Niño) is near the threshold of an extreme entropic event (4σ in the full-trajectory measure, 3σ in the endpoint measure).","tokens_in":27035,"tokens_out":5485,"duration_ms":62537,"significance":"If the underlying stochastic model and the approximations were reliable, this would be a novel application of stochastic thermodynamics to a geophysical index, with a concrete, falsifiable ranking of ENSO transitions by entropy production. The paper is self-contained in its derivations, uses publicly available data, and provides considerable technical detail in the Supplemental Material, including explicit propagator formulas and numerical simulations of the fitted model. However, the significance is limited by the fact that the path probabilities and stationary distributions used to compute entropy are all generated from the same fitted model, so the fluctuation-theorem 'verification' is an internal consistency check rather than an empirical test. The usefulness of the extreme-event classification also depends on the correctness of a heavily parameterized model with several uncontrolled approximations.","major_comments":[{"comment":"The fitted parameter b is reported with opposite signs in the two parts of the manuscript: the main text (Eq. (1) and the following line) gives b = 0.08 ± 0.01, while the Supplemental Material (section 'Computation of the Kramers-Moyal coefficients', after Eq. (19)) reports b = −0.08 ± 0.04 from the same data. The sign of b enters the transformed dynamics (Eq. (7)), the stationary density (Eq. (6)), and every forward/reverse propagator term Ω_i^F and Ω_i^R in the SM (Eqs. (41)–(54)), and therefore it changes all values of ΔS, ⟨ΔS⟩, and σ in Tables II and III. The paper does not state which value was actually used in the reported computations. This internal inconsistency makes the headline numbers irreproducible and must be resolved by recomputation or an explicit statement before the results can be assessed.","section":"Main text Eq. (1) vs SM 'Computation of the Kramers-Moyal coefficients'"},{"comment":"The main text states that transition 4 'is a 4σ event and could statistically be considered an extreme event.' However, the paper's own cumulative distribution function for transition 4, shown in Fig. 4d, has the realized value ΔS = 0.330 marked at a CDF value of approximately 0.97–0.98, which corresponds to roughly 2σ under a normal distribution, not 4σ. The σ reported in Table II (8.13 × 10^-2) gives (ΔS − ⟨ΔS⟩)/σ ≈ 4.05, but the empirical CDF built from the same model indicates that the distribution is strongly non-Gaussian and that the 4σ classification is not supported by the paper's own figure. The claim should be revised, or the discrepancy between the Gaussian-sigma calculation and the CDF must be explained.","section":"Fig. 4d and the '4σ' claim after Table II"},{"comment":"The paper presents the verification of the integral fluctuation theorem as a positive check on the analysis. Because the forward and reverse transition probabilities pF and pR are both derived from the same fitted stochastic differential equation (SM Eqs. (41)–(42)), the relation ⟨exp(−ΔS)⟩ = 1 is an identity that holds by construction when the forward and reverse path probabilities are normalized and the entropy is defined as their log ratio. This check verifies internal consistency of the numerical implementation, but it does not provide independent evidence that the model or the computed entropy values describe the actual SOI data. The text should explicitly label this as a self-consistency check rather than an empirical validation.","section":"Main text, after Table II; SM Eqs. (41)–(42)"},{"comment":"The entire entropy calculation rests on the assumption that the residual ξ_t = s_t − Φ(t) is stationary and Markovian with Kramers–Moyal coefficients exactly zero for n ≥ 3 and Gaussian white noise. The paper's validation (SM Fig. 2c,d) compares third and fourth moments of the data with simulations generated from the same fitted model; this is not an independent test of those assumptions. If real SOI fluctuations have memory (for example, due to the multi-taper reconstruction or unresolved low-frequency variability) or non-Gaussian noise, the computed path probabilities and all entropy values in Tables II and III are model artifacts rather than measured quantities. This limitation should be stated explicitly, and the Markov property and noise statistics should be checked with a data-driven, non-parametric method before the central claim is made.","section":"Main text Eq. (1); SM 'Computation of the Kramers-Moyal coefficients' and Fig. 2"}],"minor_comments":[{"comment":"The presentation contains several typos and inconsistent notation; examples include 'Jarzinsky' in Ref. [30], the missing journal information in Ref. [61], and the use of both 'integral fluctuation relations' (abstract) and 'the Integral Fluctuation Theorem' (main text) for the same quantity.","section":"Throughout"},{"comment":"The variables z and w used in the effective Kramers–Moyal coefficients are defined only after Eq. (15); moving the definitions before the equations would improve readability.","section":"SM Eqs. (15)–(18)"},{"comment":"The numeric entries use inconsistent formatting, such as '1 .61 × 10−1' and '3 .30 × 10−1' with a space after the integer part; this should be cleaned up for consistency.","section":"Tables II and III"},{"comment":"The conclusion states that transition 4 is 'the only case on the brink of being an extreme event,' but Table II also shows transitions 1 and 2 with |ΔS| above 2σ. The text should clarify that 'on the brink' refers specifically to the 4σ threshold used for extreme events, not to all deviations above 2σ.","section":"Conclusion and Table II"},{"comment":"The axis labels and tick labels in the Supplemental Material figures appear garbled (e.g., '/Minus30' instead of −30); the figures should be regenerated with proper typography.","section":"SM Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"The sign inconsistency for the fitted parameter b is a clear internal contradiction that must be fixed, and the extreme-event claim for transition 4 is contradicted by the paper's own CDF. Both issues are load-bearing for the central conclusion. The circularity of the fluctuation-theorem check is also a concern that should be addressed by reframing, though it is not by itself disqualifying. I would recommend that the editor require a revised version with recomputed numbers, an explicit statement of which parameter values were used, and a softened, properly caveated interpretation of the results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Colleague],\n\nThis paper applies stochastic thermodynamics to daily Southern Oscillation Index data, computing path entropies for the 11 recorded ENSO phase transitions and checking both integral fluctuation relations. That application is new; I do not know of prior work doing entropy fluctuations for ENSO indices, though the claim to 'inaugurate' the mindset is overblown given the existing stochastic SOI literature. The supplemental material is thorough in documenting the Kramers-Moyal fits, the protocol reconstruction, and the long propagator formulas, and the author is transparent about the modeling assumptions and the modest scope. The broad qualitative conclusion that most transitions are not extreme entropic events is plausible and survives most concerns.\n\nThe quantitative claims, however, are not yet robust. The most concrete problem is the drift coefficient b: main-text Eq. (1) reports b = +0.08 ± 0.01, while the SM fit reports b = −0.08 ± 0.04 from the same data. The sign enters the transformed drift, the stationary density, and every propagator term, so all of Tables II and III are non-reproducible as printed. This is not a modeling disagreement; it should be settled by recomputation. A second problem is that the 'verification' of the fluctuation theorems is logically empty: forward and reverse path probabilities are generated from the same fitted model, so ⟨exp(−ΔS)⟩ = 1 is an identity, not an independent check. Third, the paper calls transition 4 a 4σ event, but its own CDF in Fig. 4d shows a probability of about 0.98 at the realized ΔS, which is roughly 2σ, not 4σ. The conclusion correctly downgrades this to 'on the brink,' but the main-text claim is not supported by the figure. Fourth, parameter uncertainties are not propagated into the reported ΔS or the extremeness classification; the σ in the tables is the model's trajectory spread, not the fit uncertainty.\n\nThe transitions also differ widely in duration (from one day to several years), which makes raw path-entropy comparisons tricky; the author does compute entropy rates, which helps. None of these issues invalidates the broad finding, since the entropy values are small relative to the noise scale, but the specific extreme-event classification needs to be redone with the sign fixed and the CDF discrepancy explained.\n\nThis paper is for readers interested in stochastic thermodynamics applied to climate indicators. It deserves a serious referee, not a desk reject, but the referee should require the internal inconsistency to be fixed before publication.\n\nBest,\n[Name]","headline":"New stochastic-thermodynamics application to ENSO transitions, but an internal sign inconsistency and a tautological IFT check leave the specific extreme-event claim unverified.","tokens_in":27536,"tokens_out":5746,"would_cite":false,"duration_ms":60433,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82C31","60J60","86A10"],"pacs":["05.40.-a","05.70.Ln"],"model":"deepseek-v4-flash","headline":"The paper finds that none of the 11 recorded ENSO phase transitions since 1991 produced an extreme entropy variation; only the 1999–2000 La Niña to 2002–2003 El Niño change approaches the 4σ threshold.","keywords":["stochastic thermodynamics","entropy production","El Niño–Southern Oscillation","Southern Oscillation Index","integral fluctuation theorem","Kramers–Moyal coefficients","climate dynamics","path integrals"],"falsifier":"Refit the residual dynamics with a model that includes memory or non-Gaussian noise (for example, a nonzero third-order Kramers–Moyal coefficient or a non-Markovian term) and recompute the 11 entropy variations; if the 1999–2000 La Niña to 2002–2003 El Niño event drops below 3σ or another transition rises above 4σ, the extreme-event classification is an artifact of the stochastic model rather than a property of the data.","tokens_in":26529,"feed_emoji":"🌊","tokens_out":6039,"duration_ms":63280,"temperature":0.7,"pith_summary":"The paper asks whether the dramatic weather difference between El Niño and La Niña shows up in the entropy produced by the Southern Oscillation Index as the climate moves from one phase to the other. Using stochastic thermodynamics, it computes the entropy variation for each of the 11 recorded ENSO phase transitions in the daily SOI record, both along the full index path and from boundary values alone. It finds that none of these transitions qualifies as an extreme entropic event: most are below one-tenth of a standard deviation, and only the transition from the strong 1999–2000 La Niña to the moderate 2002–2003 El Niño sits near the extreme-event threshold. All transitions also satisfy the integral fluctuation relation, the probabilistic form of the second law. If the calculation is right, this informational entropy is decoupled from the thermal/heat picture of these climate events.","feed_headline":"No ENSO shift since 1991 was an extreme entropy event","feed_subtitle":"Daily Southern Oscillation Index paths show only the 1999–2000 La Niña to 2002–2003 El Niño change near the extreme threshold.","key_machinery":"The load-bearing object is the stochastic entropy production defined through the log-ratio of the probability of the recorded SOI trajectory under the forward protocol to its probability under the reversed protocol. To get those probabilities, the paper separates the daily SOI series $s_t$ into a deterministic climate protocol $\\Phi(t)$ (reconstructed by the Multi-Taper Method at seven significant periods) and a residual $\\xi_t = s_t - \\Phi(t)$ modelled as a stationary stochastic process with empirically fitted Kramers–Moyal coefficients. A change of variables converts the multiplicative noise into additive noise, and a path-integral (Onsager–Machlup) saddle-point approximation yields the forward and reverse transition probabilities used in the entropy ratio.","core_discovery":"The central claim is that the entropy variation $\\Delta S(\\vec s) = -\\ln[p_F(\\vec s)/p_R(\\vec s)]$ computed from forward and reverse path probabilities of the daily SOI is statistically unremarkable for all 11 ENSO transitions. Only transition 4, the strong 1999–2000 La Niña to the moderate 2002–2003 El Niño, reaches about 4σ above the mean in the full-trajectory calculation (3σ when only the endpoints are used), placing it on the brink of being an extreme event but not clearly beyond it. The paper also verifies the integral fluctuation theorem, $\\langle e^{-\\Delta S}\\rangle = 1$, in both calculation schemes, and finds no relation between the entropy variation rate and the intensity classification of the phases.","pith_inferences":["If the result survives, it implies that extreme weather associated with ENSO is not mirrored by extreme stochastic-entropy production of the SOI itself, so the index may not be the right observable for detecting thermodynamically exceptional transitions.","The same machinery could be applied to other ENSO indicators such as sea-surface-temperature indices or multivariate ENSO measures; a 4σ entropy event appearing in one of those would test whether the mildness found here is a property of the phenomenon or of the chosen index.","The boundary-only entropy variation $\\Delta\\tilde{S}(t_f,t_i)$ discards most of the signal (all but two transitions fall below $\\sigma/10$), so comparing the two tables offers a concrete way to quantify how much of the entropy information lives in the path rather than in the endpoints.","A future strong La Niña to El Niño transition similar to 1999–2000 could be monitored in real time; if its entropy variation exceeds the 4σ threshold, the paper's conclusion would shift from 'on the brink' to observed extreme behaviour."],"forward_implications":["All 11 recorded ENSO phase transitions satisfy the integral fluctuation relation in both the full-trajectory and boundary-only calculations, so the computed entropy changes are consistent with the probabilistic second law.","Most transitions have entropy variations below one-tenth of the trajectory-to-trajectory spread, so El Niño and La Niña phase shifts have so far been mild in this informational-entropy sense.","The 1999–2000 La Niña to 2002–2003 El Niño transition is the only case near the extreme threshold, making it the natural candidate for targeted study of large entropy excursions in the SOI.","The absence of a relation between entropy variation rate and the intensity classification of the phases suggests the index-based informational entropy and the thermal character of ENSO are not simply connected."],"supporting_citations":[{"why":"Supplies the daily Southern Oscillation Index series from 1991 to 2023 that all transitions and entropy calculations are based on.","marker":"[33]"},{"why":"Provides the geophysical signal-processing framework, including Multi-Taper spectral estimation, used to reconstruct the climate protocol $\\Phi(t)$.","marker":"[36]"},{"why":"Gives the sampling-rate-adjusted Kramers–Moyal coefficient formulas that let the paper fit the stochastic dynamics of $\\xi_t$ from daily data.","marker":"[48]"},{"why":"Provides the path-integral formulation whose saddle-point approximation yields the forward and reverse transition probabilities entering the entropy ratio.","marker":"[51]"},{"why":"Supplies the definition of trajectory entropy variation as the log-ratio of forward to reverse path probabilities used in Eq. (4).","marker":"[49]"},{"why":"Supplies the intensity classification identifying the 1999–2000 La Niña as strong and the 2002–2003 El Niño as moderate.","marker":"[61]"}],"fun_headline_variants":["ENSO shifts: entropy never extreme except one near-miss","One ENSO transition flirts with extreme entropy","ENSO data: only one path nears entropy extreme","No extreme entropy in ENSO shifts except one borderline"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that after subtracting the climate protocol the daily SOI fluctuations are a stationary Markov process driven by Gaussian white noise with no third- or higher-order Kramers–Moyal coefficients, so the fitted model, not the raw data alone, fixes the path probabilities and hence the entropy values.","fun_headline_variants_meta":{"raw":{"variants":["ENSO shifts: entropy never extreme except one near-miss","One ENSO transition flirts with extreme entropy","ENSO data: only one path nears entropy extreme","No extreme entropy in ENSO shifts except one borderline"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000561,"raw_usage":{"total_tokens":2620,"prompt_tokens":859,"completion_tokens":1761,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":475,"completion_tokens_details":{"reasoning_tokens":1696}},"tokens_in":475,"tokens_out":1761,"duration_ms":15044,"temperature":1.0,"reasoning_tokens":1696,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:29:23.864333+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Refit the residual dynamics with a model that includes memory or non-Gaussian noise (for example, a nonzero third-order Kramers–Moyal coefficient or a non-Markovian term) and recompute the 11 entropy variations; if the 1999–2000 La Niña to 2002–2003 El Niño event drops below 3σ or another transition rises above 4σ, the extreme-event classification is an artifact of the stochastic model rather than a property of the data.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the daily Southern Oscillation Index series from 1991 to 2023 that all transitions and entropy calculations are based on."},{"cited_title":"Ghil, M.R","cited_arxiv_id":null,"evidence_quote":"Provides the geophysical signal-processing framework, including Multi-Taper spectral estimation, used to reconstruct the climate protocol $\\Phi(t)$."},{"cited_title":"Anteneodo and S.M","cited_arxiv_id":null,"evidence_quote":"Gives the sampling-rate-adjusted Kramers–Moyal coefficient formulas that let the paper fit the stochastic dynamics of $\\xi_t$ from daily data."},{"cited_title":"Wio, Path Integrals for Stochastic Processes: An In- troduction","cited_arxiv_id":null,"evidence_quote":"Provides the path-integral formulation whose saddle-point approximation yields the forward and reverse transition probabilities entering the entropy ratio."},{"cited_title":"Spinney and I","cited_arxiv_id":null,"evidence_quote":"Supplies the definition of trajectory entropy variation as the log-ratio of forward to reverse path probabilities used in Eq. (4)."},{"cited_title":"Classification regarding the impact of the events can be found in Ref","cited_arxiv_id":null,"evidence_quote":"Supplies the intensity classification identifying the 1999–2000 La Niña as strong and the 2002–2003 El Niño as moderate."}],"review_version":1}