{"id":"d1b09d17-ac6b-4c88-9faf-414d9d6161f6","arxiv_id":"2607.27299","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Under measurement noise, trajectory-based information bounds for feedback engines fail faster than instantaneous-correlation bounds, making the simple Markovian mutual-information bound the tightest over a broad noise range.","lead":"An experiment on a vibrating-cantilever information engine shows that when measurements get noisy, the elaborate bounds that track the full measurement history lose their edge, and a simpler bound based on instantaneous correlations becomes the tightest constraint on extracted work. The result tells experimentalists which thermodynamic formula to trust in realistic, noisy feedback devices.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Finite-memory plateau for H and J may reflect bias cancellation, not true entropy rates; the crossover in Fig. 1 could be an estimation artifact.","rationale":"The reader's weakest_assumption prioritized the identification y=c and the generalization from a single binary measurement model, with finite-memory truncation noted as a secondary risk. I agree that the model choice limits the generality, but the most load-bearing concern is the finite-memory estimation of H and J because it directly affects the quantitative crossover that is the paper's central evidence. If the plateau values are biased, the crossover between I_u−I and −Δ_mI may not exist at all, undermining the main claim even within the chosen model. The reader's conditional verdict already accounts for data/code availability and missing SI, but the finite-memory issue is more specific and testable: it can be resolved by computing exact entropy rates for the fully specified stochastic dynamics. I therefore maintain the verdict at CONDITIONAL (UNCHANGED) because the concern is serious but addressable, and the paper's internal consistency and experimental data make a definitive rejection premature until the entropy-rate validation is performed.","tokens_in":15923,"tokens_out":10564,"duration_ms":87254,"concrete_test":"Generate long synthetic trajectories from the underdamped Langevin dynamics (Eqs. 11–12) with the same measurement model (Eq. 18), and compute the exact entropy rate H_exact of the binary control sequence c_n using the optimal forward-filtering recursion for the hidden Markov model (continuous state, discrete output), averaging over a long simulation. Compare H_exact with the plateau value of H_M in Fig. 6. Also compute J_exact by the analogous forward recursion for the backward process, and recompute the bound I_u−I as a function of Δx. If H_exact differs from the plateau by more than a few percent, or if the recomputed crossover shifts markedly (or disappears), the finite-memory estimation is the cause. A cheaper complementary check: re-estimate H_M with 100× longer trajectories and M up to 15; if H_M continues to decrease beyond the reported plateau, the plateau is an artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim—the crossover between the unavailable-information bound I_u−I and the Markovian bound −Δ_mI as measurement noise Δx increases—depends on accurate values of the entropy rate H of the control sequence and the backward cross-entropy rate J. Both are estimated via finite-memory plug-in estimators (H_M, J_M) with a plateau identified for M ≤ M_max, beyond which sample sizes are insufficient. However, plug-in entropy estimators have downward finite-sample bias that grows with the number of conditioning states (2^M), while truncation bias (finite M) makes the true conditional entropy decrease with M. These biases act in opposite directions and can cancel, producing a spurious plateau at a value that is not the true H. If the reported plateau overestimates H, then I_u−I = J−H is underestimated (too negative), making the unavailable-information bound appear looser than it truly is; the Markovian bound is not subject to this memory bias because it uses only instantaneous distributions. The theoretical solid lines in Fig. 1 are computed with the same estimators, so both theory and experiment share the bias. For the shortest sampling interval (Δt_m/τ_rel=0.22), M_max covers only ~1.3 τ_rel of memory, which may be insufficient if correlations decay more slowly than assumed. No exact entropy-rate computation (e.g., via the HMM forward-filtering recursion) is provided to validate the plateau. Thus, the existence and location of the crossover—the paper's headline result—rest on an unvalidated estimation assumption.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies an underdamped feedback-controlled micro-cantilever with binary position measurements, where the measured outcome directly sets the control variable (c = ±1). It compares three second-law refinements — the transfer-entropy bound, the unavailable-information bound, and the Markovian mutual-information bound — as functions of measurement noise Δx and sampling interval Δt_m, using both experimental data and Kramers-equation-based theory. The central claim is that none of the three bounds is universally optimal: at low noise the unavailable-information bound is tightest, but as measurement noise increases, trajectory-dependent bounds (especially unavailable information) degrade faster than the instantaneous Markovian bound, producing a crossover in which the Markovian bound becomes tightest over a broad noise range. The paper interprets this as evidence for a general limitation of trajectory-statistics-based information-thermodynamic descriptions in realistic noisy feedback.","tokens_in":16133,"tokens_out":5536,"duration_ms":50017,"significance":"If the central claim is correct, the paper makes a valuable contribution: it shows that the tightness of thermodynamic information bounds is not an intrinsic property of the information measure but depends on how measurement noise interacts with temporal correlations. It also provides a methodological advance by estimating non-Markovian entropy and unavailable-information rates directly from experimental data, and it gives analytic results in the long-sampling-time limit. A notable strength is that the theoretical curves in Fig. 1 are computed from Kramers-equation solutions with parameters fixed by the experimental setup, with no free parameter fitted to the measured work. The conclusions are of broad interest to stochastic thermodynamics and experimental information engines. However, the headline crossover depends on the accuracy of finite-memory entropy-rate estimators, and the generality of the claim rests on a single coarse-graining choice; both points need additional support before the central claim is fully established.","major_comments":[{"comment":"The crossover in Fig. 1 relies on the plateau values of H_M and J_M being accurate estimators of the true entropy rates H and J. For a fixed M, plug-in conditional-entropy estimators have downward finite-sample bias, while the true conditional entropy decreases as M increases; these two opposing biases can cancel and produce a plateau at a value that is not the true H. If H is overestimated, then I_u - I = J - H is underestimated (too negative), making the unavailable-information bound appear looser exactly in the noise regime where the crossover is claimed. The theoretical solid lines in Fig. 1 are computed with the same finite-memory estimators, so they do not independently validate the plateau. For the shortest sampling interval (Δt_m/τ_rel = 0.22), the usable memory is particularly limited and truncation bias is most dangerous. The manuscript should provide an independent validation","section":"Section I, \"minimal model\" with y = c; Section V Discussion"},{"comment":"The abstract and Discussion claim a 'general limitation' of trajectory-based information-theoretic descriptions under measurement noise. However, all quantitative results are computed within the minimal model in which the measurement outcome is identified with the control variable, y = c. The Discussion itself concedes that other coarse-grainings 'could quantitatively affect the values of the information measures.' The generality is therefore asserted from a mechanism argument, not demonstrated. To support the headline claim, the paper should either test at least one alternative measurement variable or coarse-graining (e.g., a multi-threshold or continuous measurement variable) and show that the same qualitative crossover appears, or provide an analytic argument independent of the specific choice of y. Absent that, the conclusion should be restricted to the minimal model or explicitly fr","section":"Section II, Methods, \"Finite-memory estimators\"; Fig. 6"},{"comment":"The finite-memory approximation of the backward process, Eq. (31), conditions on the time-reversed forward sequence only through a memory window of length M+1. The unavailable-information estimator J_M is therefore sensitive not only to the forward-memory truncation but also to the initial-condition prescription for the backward process, P(Γ_1^R | c†_k) = P(Γ_k | c_k). The text states that backward trajectories were generated for each forward trajectory, but it is not explained how finite-length forward trajectories affect the convergence of J_M to its asymptotic rate. If boundary or initial-condition effects decay more slowly than the memory window, the plateau in J_M could be systematically biased. The authors should provide a boundary-effect analysis or demonstrate that J_M is insensitive to the backward initial condition.","section":"Methods, \"Finite-memory estimators\", Eq. (32); Section IV A"}],"minor_comments":[{"comment":"Please specify the number of feedback cycles used for each experimental point, the meaning of the error bars, and the normalization of Δx (in units of σ). The statement that error bars are invisible is not sufficient; a representative error bar or an inset would help the reader assess statistical accuracy.","section":"Fig. 6 caption"},{"comment":"Please define M_max explicitly and state the criterion used to mark points as 'crossed out' (insufficient statistics). Also report the sample size N in the caption or in the Methods, since the plateau identification is central to the claims.","section":"Methods, \"Finite-memory estimators\", Eq. (32)"},{"comment":"The overline notation is used both for per-cycle averages and for time-reversed sequences (⃗ y†). This is occasionally confusing, for example in Eqs. (4) and (7). A different symbol for time reversal would improve readability.","section":"Section II, Eqs. (4) and (7)"},{"comment":"The footnote defining singular measurements appears after the reference list; it should be placed as a proper footnote in the main text or integrated into the Methods.","section":"References/Footnotes"},{"comment":"The statement 'Data supporting this study will be available in an open public repository upon acceptance' is acceptable for a journal submission, but given the central role of the experimental estimators, a statement about code availability for the estimators (e.g., for H_M and J_M) would strengthen reproducibility.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses an important question and the experimental platform is well suited to it. My main concern is not the thermodynamic framework but the robustness of the finite-memory entropy-rate estimates, which directly determine the crossover that is the central claim. The authors should be asked to validate H and J by an independent method (e.g., HMM forward filtering or much longer simulations) and to quantify the bias. I would also encourage them to either soften the generality claim or provide evidence for at least one alternative coarse-graining. These are load-bearing but fixable within the scope of the manuscript."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know before you read it. It's a serious experiment-plus-theory paper, no free parameters fitted to the work, and the central crossover between trajectory-based bounds and the instantaneous mutual-information bound is new. The catch is that the crossover depends on finite-memory estimates of entropy rates that are not independently validated.\n\nThe good parts: the experimental setup is clean, the underdamped cantilever with tunable noise and three sampling intervals covers the right parameter space. The long-sampling-time limit gives analytic expressions for all three bounds, which cross-check the estimators. The theory lines and the data agree without any parameter adjustment. The finding that the Markovian bound becomes tightest over a broad noise range, and that its sign change tracks the loss of work extraction, is genuinely interesting.\n\nThe soft spot is the plateau identification for H and J. Plug-in entropy estimators have finite-sample bias that grows with memory length, and the plateau you see for M up to M_max could in principle be bias cancelling the true decrease of conditional entropy, rather than convergence. The theory curves use the same estimators, so a bias would be shared and would not show up as a mismatch. No exact entropy-rate computation (e.g., via HMM filtering) is provided to prove the plateau is real. For the shortest sampling interval, M_max covers about 1.3 relaxation times, which may be enough but is not demonstrated. This is not necessarily fatal, but it is load-bearing for the crossover. A referee should ask for a sensitivity analysis or an exact calculation.\n\nTwo smaller issues. The generic claim about trajectory-based bounds is argued from a single binary measurement model with uniform noise; the authors themselves concede that other coarse-grainings could change the numbers. That limits the scope more than they acknowledge. And the proofs for the underdamped ordering and saturation are in the SI, which is not included in the preprint, so they cannot be checked yet.\n\nBottom line: this deserves a serious referee. The experimental methodology and the comparison itself are valuable even if the crossover shifts a little. The main thing I would ask for is exact entropy-rate validation and the SI. I'd bring it to reading group, but I would not cite it in my own work until that validation is public.","headline":"A serious experiment-plus-theory paper whose headline crossover is credible but rests on finite-memory entropy estimates that need independent validation.","tokens_in":16739,"tokens_out":5224,"would_cite":false,"duration_ms":43733,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["05.70.Ln","05.40.-a","89.70.Cf"],"model":"deepseek-v4-flash","headline":"In a noisy feedback engine, the simple instantaneous mutual-information bound becomes the tightest constraint on extracted work once measurement noise grows.","keywords":["information thermodynamics","feedback control","measurement noise","unavailable information","transfer entropy","Markovian mutual information","underdamped oscillator","non-Markovian control"],"falsifier":"Compute or measure the three bounds under the same noise model but with a measurement variable that is not the control decision (e.g., a threshold on a combination of position and velocity, or a multi-level output). If the unavailable-information bound remains tighter than the Markovian mutual-information bound at high noise, the predicted crossover is specific to y=c rather than a general property of trajectory-based bounds.","tokens_in":15680,"feed_emoji":"⚡","tokens_out":4869,"duration_ms":39892,"temperature":0.7,"pith_summary":"This paper asks which information-theoretic refinement of the second law remains most useful when feedback control is realistic: measurements are noisy and control decisions are temporally correlated. In an underdamped micro-cantilever engine, the authors compare three bounds on extracted work—transfer entropy, unavailable information, and Markovian mutual information—and show that none is universally optimal. The central finding is that measurement noise degrades trajectory-based bounds (transfer entropy and unavailable information) much faster than the instantaneous Markovian mutual-information bound, so the Markovian bound becomes the tightest over a broad noise range. The paper also shows that the sign change of the Markovian bound tracks the noise level at which work extraction ceases, and develops finite-memory estimators that make non-Markovian information rates experimentally accessible. If correct, it means the thermodynamic value of a given information measure is not intrinsic but depends on how noise degrades the trajectory statistics it relies on.","feed_headline":"Noise makes the simplest information bound the tightest","feed_subtitle":"In a cantilever feedback engine, instantaneous mutual information beats detailed trajectory bounds once measurement noise grows.","key_machinery":"The argument is carried by three information-theoretic bounds on extracted work per cycle: the transfer-entropy rate I_c, the unavailable-information correction I_u − I, and the Markovian mutual-information term −Δ_m I. The first two depend on the full control sequence (trajectory-based); the third depends only on instantaneous pre- and post-measurement correlations. The load-bearing theoretical result is the inequality −Δ_m I ≥ −I_c for both perfect and imperfect measurements (Eq. 10), plus the numerically and experimentally established crossover between I_u − I and −Δ_m I. Estimating the trajectory-based rates requires finite-memory estimators, which plateau once the memory length exceeds","core_discovery":"On the paper's own terms: in an underdamped feedback engine with Markovian measurements and non-Markovian control, the three standard second-law refinements—transfer entropy, unavailable information, and Markovian mutual information—are all valid inequalities but have no universal ordering. For perfect measurements the unavailable-information bound is the tightest, but as measurement noise grows the trajectory-dependent unavailable-information bound degrades fastest, and the instantaneous Markovian mutual-information bound becomes the tightest over a broad range of noise. The transfer-entropy bound always remains looser than the Markovian one, while the unavailable-information bound can even","pith_inferences":["If the mechanism is generic, the same crossover should appear for other measurement variables and noise models; a direct test would be to compute the bounds with a different binary measurement (e.g., based on velocity or a threshold other than the origin) and check whether the unavailable-information bound remains the tightest at high noise.","The result suggests that feedback protocols designed to exploit temporal correlations should be evaluated with noise-aware information measures; optimizing for zero-noise tightness may be misleading.","The finite-memory plateau method could be transferred to other experimental systems with non-Markovian feedback, including biological sensors, to quantify how much trajectory information survives noise.","A possible extension: for non-uniform noise distributions or multi-state measurements, the crossover noise level may shift; mapping the crossover as a function of noise model would test the claimed generality."],"forward_implications":["In noisy regimes, the simpler instantaneous mutual-information bound is tighter than the unavailable-information bound, so information engines need not be analyzed with full trajectory statistics.","The unavailable-information bound, exactly tight for idealized perfect measurements in overdamped systems, does not survive under measurement noise as the tightest constraint.","The sign of the Markovian mutual-information bound correctly locates the noise threshold at which work extraction stops, giving an experimentally useful diagnostic.","Trajectory-dependent bounds (transfer entropy and unavailable information) require increasingly detailed statistics that measurement noise selectively degrades; no single information measure is universally optimal.","Finite-memory estimators allow direct experimental estimation of entropy and unavailable-information rates in non-Markovian control sequences, enabling comparisons that were previously out of reach."],"fun_headline_variants":["Noise flips which info bound is tightest in feedback engines","Trajectory info bounds fail under noise; instant correlation wins","Measurement noise favors simple info bounds over detailed ones","When noise grows, Markovian bound beats unavailable info bound","Noisy feedback? The simplest thermodynamic bound wins"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The paper's headline generalization rests on the minimal model in which the measurement outcome is identified with the control variable (y=c); the authors note that another coarse-graining could quantitatively change the information values, so the crossover could in principle be an artifact of that choice.","fun_headline_variants_meta":{"raw":{"variants":["Noise flips which info bound is tightest in feedback engines","Trajectory info bounds fail under noise; instant correlation wins","Measurement noise favors simple info bounds over detailed ones","When noise grows, Markovian bound beats unavailable info bound","Noisy feedback? The simplest thermodynamic bound wins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000138,"raw_usage":{"total_tokens":962,"prompt_tokens":689,"completion_tokens":273,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":433,"completion_tokens_details":{"reasoning_tokens":193}},"tokens_in":433,"tokens_out":273,"duration_ms":8090,"temperature":1.0,"reasoning_tokens":193,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T10:00:38.725684+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute or measure the three bounds under the same noise model but with a measurement variable that is not the control decision (e.g., a threshold on a combination of position and velocity, or a multi-level output). If the unavailable-information bound remains tighter than the Markovian mutual-information bound at high noise, the predicted crossover is specific to y=c rather than a general property of trajectory-based bounds.","supporting_citations":[],"review_version":1}