{"id":"307f2265-c172-4fcc-b5af-9a44e912e06f","arxiv_id":"2511.09183","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Displacements grouped by starting and ending location yield a model-free Kullback-Leibler measure of irreversibility that bounds entropy production and can be measured from single-molecule data.","lead":"The authors show that grouping a molecule's measured jumps by where they start and end gives a model-free readout of how irreversible its dynamics are, with no need for the underlying forces or diffusion coefficient. Because the readout is a lower bound on entropy production and can be estimated from single-molecule force spectroscopy traces, it offers a practical non-equilibrium fingerprint for protein folding and other stochastic systems.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Finite-Δt protocol artifact: Eq. A13's same-protocol 'time reversal' is only valid at Δt→0, yet experiments use Δt=5 ms; reported unfolding/refolding asymmetry may be contaminated.","rationale":"The stationary-system theory is sound: Eq. (12) follows from the data-processing inequality, and SM-I shows equality for 1D time-independent Langevin systems. The proof for time-dependent protocols, however, is explicitly limited to Δt→0, and the authors themselves acknowledge overestimation at finite Δt (Fig. 3(c) inset, Appendix A1b). The experiments use Δt=5 ms, where the bound is not guaranteed and where the comparison in Eq. A13 is not a true time reversal because the protocol is not reversed. Since the boundary position is selected per ramp to maximize measured irreversibility, the finite-Δt excess could inflate the unfolding-versus-refolding asymmetry in R3 IVVI. This concern does not overturn the paper: the Crooks-based cross-validation in Fig. S13 supports the qualitative trends, and the stationary NESS results are independent of the issue. But the specific experimental claim that the method resolves landscape asymmetry is not fully settled without a finite-Δt control or a reverse-protocol check. This is consistent with the reader's CONDITIONAL verdict, so no change is needed.","tokens_in":36670,"tokens_out":6230,"duration_ms":70976,"concrete_test":"In the Fig. 4(e) asymmetric-potential simulations, compute Σ_{Δt,t} from Eq. A13 at Δt=5 ms and compare it to the exact ⟨ΔS_tot⟩(t) available in simulation, and to a version using the true time-reversed protocol: replace q_{Δt,t}(−ℓ,C̃) with displacements from trajectories run under the reversed force ramp, measured in the corresponding time window. Repeat for Δt=1 ms and 2 ms. If the mutant-like unfolding-minus-refolding difference retains its sign and magnitude at Δt→0, or under the reverse-protocol denominator, the finite-Δt artifact is not decisive; if it shrinks or flips, the experimental asymmetry is a protocol artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Appendix A1b states explicitly that for time-dependent driving the bound holds only as Δt→0 and that for larger intervals it is not valid; Fig. 3(c) inset shows Σ exceeding true entropy for r=±20 pN/s low-barrier. The experimental analysis nevertheless uses Δt=5 ms (Section IV C) and compares q_{Δt,t−Δt}(ℓ,C) with q_{Δt,t}(−ℓ,C̃) measured under the same forward protocol (Eq. A13), not under the reverse protocol. The difference between these distributions contains both genuine irreversibility and a protocol-shift term O(r Δt^{3/2}) that vanishes only in the limit. No finite-Δt correction is applied, and the boundary k is chosen per ramp to maximize ΔΣ (SM-X), so the excess can be unevenly distributed between unfolding and refolding. The reported asymmetry for R3 IVVI (Fig. 4d) is exactly the kind of comparison this uncontrolled excess could bias. Although Crooks cross-validation (Fig. S13) supports the overall trend, it does not validate the peak shapes or the magnitude of the asymmetry. Thus the central experimental inference is conditional on controlling the finite-Δt/protocol-reversal artifact.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a coarse-grained irreversibility measure Σ_Δt(C_n) (Eq. (10)) based on the Kullback-Leibler divergence between displacement distributions categorized by initial/final side of spatial boundaries and their time reverses. It proves that for stationary overdamped Langevin systems Σ_Δt is a lower bound on average entropy production (Eq. (12)), that a hierarchy of refined partitions tightens the bound (Eq. (13)), and that in the short-time limit a conditional fluctuation theorem holds (Eq. (11)). For time-dependent protocols, the same estimator is shown to bound entropy production only as Δt→0 (Appendix A1b). The method is applied to magnetic-tweezer unfolding/refolding of talin R3 under force ramps, reporting that the mechanically stabilized mutant R3 IVVI is more irreversible upon unfolding than refolding, an asymmetry reproduced by simulations with an asymmetric double-well potential.","tokens_in":37045,"tokens_out":6590,"duration_ms":68993,"significance":"The stationary lower-bound theorem is clean and self-contained, and the hierarchy via the data-processing inequality is elegant. The estimator is genuinely model-free in that it does not require forces, the diffusion coefficient, or full trajectories; the paper demonstrates on an analytically solvable NESS that it outperforms a direct TUR bound. The inclusion of a nearest-neighbor DKL estimator with a public code repository and the cross-validation of the experimental trends with Crooks' fluctuation theorem (Fig. S13) are notable strengths. If the finite-Δt limitation for time-dependent protocols is properly controlled, the method could be a widely applicable tool for single-molecule and tracking experiments.","major_comments":[{"comment":"The generalized estimator for time-dependent protocols is proven to bound entropy production only in the Δt→0 limit. Section IV C uses Δt=5 ms, and Fig. 3(c) (low-barrier, r=±20 pN/s) shows the estimator exceeding ⟨ΔS_tot⟩. The comparison in Eq. (A13) contains a protocol-shift term O(r Δt^{3/2}) that is not controlled. This affects the central experimental inference of an unfolding/refolding asymmetry (Fig. 4d), because the artifact can be unevenly distributed between ramps. Since the simulations in Fig. 4(f,g) use the same estimator, their agreement with experiment does not by itself validate the asymmetry. The authors should provide a quantitative finite-Δt correction or error bound, or demonstrate that the reported asymmetry is insensitive to Δt and to the protocol-shift term estimated from the measured ramp rates.","section":"Appendix A1b, Eq. (A13); Section IV C"},{"comment":"The boundary k is chosen separately for each ramp and condition by maximizing ΔΣ_tf (or ΔΣ^trans_tf). For a stationary system this is harmless because every k gives a lower bound; for time-dependent finite Δt, however, no such bound exists, and optimizing k can systematically inflate the estimate. Since different k values are used for unfolding and refolding (e.g., 24 nm vs 19 nm for R3 IVVI at ±10 pN/s), the selection procedure can bias the asymmetry the paper reports. A robustness check using a common, physically motivated k (e.g., the transition-state location) or a pre-registered selection rule independent of the measured asymmetry should be provided.","section":"SM-X, Section IV C"},{"comment":"The comparison between R3 WT and R3 IVVI total irreversibility uses different force windows (3–13 pN vs 4–20 pN) and different numbers of trajectories. The total entropy production over a ramp depends on the protocol range, so the estimator magnitude is not directly comparable across constructs without normalization. Although the Crooks cross-validation in Fig. S13 supports the overall trend, the paper should explicitly discuss whether the reported difference in ΔΣ_tf between WT and IVVI is partly a protocol-range effect rather than a purely molecular one.","section":"Section IV C, Figs. 4(d) and S13"}],"minor_comments":[{"comment":"The text correctly states that for time-dependent driving the bound holds only as Δt→0, but the simulation curves in Fig. 3(c) are presented as dissipation rates without always repeating this caveat. Adding an explicit caveat in the figure caption and in the corresponding results text would help readers avoid over-interpreting the finite-Δt values.","section":"Section IV B / Fig. 3(c)"},{"comment":"The sentence 'with P(x|x′) = P(x|x′) and P(˜x|xN)=P(x′|x)' contains an apparent typo; the first equality should presumably involve the time-marginalized propagator or a different symbol. Please correct.","section":"SM-I, near Eq. (S9)"},{"comment":"The choice Δt=5 ms is motivated by simulations, but Fig. S8 shows that at Δt=5 ms the r=±5 pN/s points for R3 IVVI are quite close. The paper should explicitly address the uncertainty of the ranking at this timescale, especially since the main-text asymmetry claim rests on comparisons across rates.","section":"Fig. S8 / Section IV C"},{"comment":"The time-reversal class mapping C→C̃ is used in Eq. (10) but is not formally defined in the main text until the footnote after Eq. (10). Please define it explicitly before the definition of Σ_Δt.","section":"Section III B"}],"recommendation":"major_revision","confidential_remarks":"This is a solid stochastic thermodynamics paper with a strong theoretical core. My recommendation for major revision is driven by the gap between the rigorously proven stationary/short-time results and the finite-Δt experimental claims; this gap is acknowledged in Appendix A1b but not quantitatively controlled. The Crooks cross-validation is convincing support for the overall trend, but the paper would be strengthened by making it the primary validation of the asymmetry and by adding a finite-Δt error analysis. The paper is well within the journal's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, what to know: this paper gives you a way to estimate entropy production from displacement histograms without knowing forces or diffusion coefficients. The core estimator Σ_Δt(C_n) is a Kullback-Leibler divergence between forward and time-reversed displacement-class distributions, and the proof that it lower-bounds entropy production for stationary overdamped Langevin systems is clean and self-contained. The hierarchy of bounds under class merging is a nice touch, though the data-processing inequality behind it is standard. The short-time conditional fluctuation theorem and the local dissipation expansion (Eq. 15) put the estimator on firmer theoretical footing than most ad hoc measures. Code is on GitHub, which helps reproducibility.\n\nThe experimental part is the real novelty. They measure talin R3 wild-type and IVVI mutant under force ramps in magnetic tweezers, thousands of cycles, and show that the estimator tracks the expected dissipation peaks at unfolding/refolding transitions. The cross-validation with Crooks' fluctuation theorem (Fig. S13) independently confirms the main trends: faster ramps dissipate more, the mutant dissipates more overall, and in the mutant unfolding is more irreversible than refolding. That is genuine supporting evidence, and it's a nice demonstration.\n\nThe soft spots are in proportion: the experiment uses Δt = 5 ms, but the proof for time-dependent ramps holds only as Δt → 0. The paper says so in App. A1b and shows the estimator can exceed true entropy production for fast ramps (Fig. 3c inset). That is an acknowledged limitation, not a hidden one. The stress-test worry about the protocol-shift term is real—the same-protocol time reversal in Eq. A13 is an approximation at finite Δt—but the paper doesn't oversell it; they present the trends as robust across Δt. The boundary k is chosen per ramp to maximize Σ, which could bias the unfolding-vs-refolding comparison, and the asymmetric simulation potential is selected to reproduce the experimental asymmetry, so the landscape interpretation is more illustrative than falsifiable. Given the Crooks cross-check, I'd call the asymmetry claim plausible but not definitive.\n\nOverall: a solid, useful tool with a clean core proof and an honest experimental demonstration. The central theoretical claim holds up. My only hesitation is that the specific conclusion about the talin landscape is weaker than the abstract implies, but the paper itself acknowledges the main caveats.\n\nRecommendation: yes, send to peer review. A serious referee will find the theory clean and the experiment valuable. The authors should be pushed to quantify the finite-Δt error for their specific conditions and to justify the boundary selection procedure, but this is publishable work.","headline":"A practical, model-free irreversibility estimator with a clean proof and a real single-molecule test; the finite-Δt caveat and parameter choices temper the landscape claim but don't sink the paper.","tokens_in":37470,"tokens_out":2669,"would_cite":true,"duration_ms":26128,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82C31","60J60"],"pacs":["05.40.-a","05.70.Ln"],"model":"deepseek-v4-flash","headline":"Sorting single-molecule displacements into spatial classes gives a model-free, experimentally accessible lower bound on entropy production.","keywords":["irreversibility","entropy production","Langevin dynamics","displacement distributions","Kullback-Leibler divergence","fluctuation theorem","single-molecule force spectroscopy","magnetic tweezers"],"falsifier":"Take the low-barrier double-well system of Fig. 3 with r = ±20 pN/s, compute the exact average entropy production in each ramp, and evaluate ΣΔt(C4) at Δt = 5 ms and at several smaller Δt values. Extrapolate Σ to Δt → 0 and compare the extrapolated total with the true entropy production; if the extrapolated value differs systematically from the true value, or if the 5 ms measurement exceeds the true value (as the inset shows it can), then the finite-resolution protocol does not measure entropy production directly and any ranking of conditions would need a Δt-dependent correction.","tokens_in":36616,"feed_emoji":"🧬","tokens_out":8101,"duration_ms":81024,"temperature":0.7,"pith_summary":"A stochastic system's dissipation is usually hidden behind forces and diffusion coefficients that are hard to measure. This paper argues that the irreversibility of an overdamped Langevin process can be read off directly from displacement statistics: record where a molecule starts and ends over a short interval, sort those displacements into a few classes defined by spatial boundaries, and compare each class's displacement distribution with its time-reversed counterpart. The resulting Kullback-Leibler divergence is shown to be a lower bound on average entropy production for stationary systems and in the short-time limit for time-dependent driving, and the bound tightens monotonically as more classes are added. The same logic, applied only to boundary-crossing counts, recovers the spatial profile of dissipation. The paper then applies the estimator to magnetic-tweezer unfolding and refolding of the protein talin R3, where it resolves that a mechanically stabilized mutant dissipates more when unfolding than when refolding—an asymmetry traced to an asymmetric free-energy landscape. A sympathetic reader would care because, if this works, it gives experimentalists a way to quantify thermodynamic cost from ordinary position traces, with no model of the energy landscape required.","feed_headline":"Few displacement bins reveal a molecule's true entropy cost","feed_subtitle":"A dissipation lower bound from position traces alone tells which folding direction wastes more energy.","key_machinery":"Equation (10): ΣΔt(Cn) = k_B ∑_{C∈Cn} ∫ dℓ q(ℓ,C) ln[q(ℓ,C)/q(−ℓ, C̃)]. It is the Kullback-Leibler divergence between the forward and time-reversed displacement statistics, where displacements are binned into classes defined by the initial and final positions relative to spatial boundaries (e.g., crossing a boundary left-to-right vs right-to-left, or staying in the bulk). This object does the work of converting raw position-time data into a number that tracks entropy production, and the same machinery yields the local dissipation profile via Eq. (14)-(15), counting only the probability fluxes across a boundary. The mathematical engine behind the bounds is the log-sum inequality: each coarse-","core_discovery":"The central claim is that the mixed discrete-continuous Kullback-Leibler divergence ΣΔt(Cn) — defined by summing over displacement classes C the integral over displacement length ℓ of q(ℓ,C) ln[q(ℓ,C)/q(−ℓ, C̃)] — captures the irreversibility of an overdamped Langevin system at finite temporal resolution. Because q(ℓ,C) is the joint probability of observing a displacement ℓ that belongs to a specified spatial class, it can be estimated directly from experimental trajectories. The authors prove, via the log-sum inequality applied to the two coarse-graining steps (projecting paths onto their endpoints, then projecting endpoints onto ℓ and class), that for stationary systems ΣΔt(Cn) ≤ ⟨ΔS_tot⟩,","pith_inferences":["If the bound is approximately tight for a given partition, the gap between Σ and true entropy could be used as a quantitative measure of how much information about dissipation lives in the path interior rather than the endpoints; in one-dimensional stationary systems the gap vanishes, so the estimator may also serve as a Markovianity probe in more complex settings.","The unfolding/refolding asymmetry of the mutant implies that the barrier lies closer to the folded basin; this suggests a practical route to infer transition-state positions from non-equilibrium cyclic experiments, applicable to other mechanosensitive proteins without free-energy reconstruction.","Scanning over the observation window Δt may reveal hidden fast timescales: if two different Δt values give different rankings among conditions, the system possesses relaxation processes between the two timescales, and the method could be used as a multi-scale probe.","One stress-test is to apply the estimator to systems with non-Markovian or active noise; the identification of time-reversed classes should break down, but the raw asymmetry of displacement distributions may still be a useful dimensionless index for comparing far-from-equilibrium activity."],"forward_implications":["For any stationary overdamped Langevin system, the estimator requires no knowledge of forces, potentials, or diffusion coefficient, and its measured value never exceeds the true average entropy production.","Adding more displacement classes always tightens the lower bound, so experimentalists can trade off data volume against tightness of the inferred dissipation.","In time-dependent single-molecule experiments, the estimator's peaks in time coincide with the moments of unfolding and refolding transitions, and its cumulative value ranks pulling rates and protein variants by irreversibility.","The method provides a spatial map of dissipation: by scanning the boundary position, one obtains the local entropy production rate at each point of the reaction coordinate.","Because the estimate relies only on displacement statistics, it can be cross-checked against dissipated work measured from forward and reverse protocols without exponential reweighting."],"fun_headline_variants":["Displacement bins yield model-free entropy bound","Few categories reveal system's irreversible cost","Position traces alone lower-bound dissipation","Binning displacements measures irreversibility directly","Single-molecule paths expose energy waste bounds"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"Under time-dependent driving, the estimator treats displacements measured in two consecutive time windows as forward and reversed copies of the same process, an identification that is valid only in the limit of vanishing time step, so finite experimental resolution can make the measured irreversibility exceed the true entropy production.","fun_headline_variants_meta":{"raw":{"variants":["Displacement bins yield model-free entropy bound","Few categories reveal system's irreversible cost","Position traces alone lower-bound dissipation","Binning displacements measures irreversibility directly","Single-molecule paths expose energy waste bounds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000252,"raw_usage":{"total_tokens":1381,"prompt_tokens":711,"completion_tokens":670,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":455,"completion_tokens_details":{"reasoning_tokens":621}},"tokens_in":455,"tokens_out":670,"duration_ms":6126,"temperature":1.0,"reasoning_tokens":621,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T22:40:11.302483+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the low-barrier double-well system of Fig. 3 with r = ±20 pN/s, compute the exact average entropy production in each ramp, and evaluate ΣΔt(C4) at Δt = 5 ms and at several smaller Δt values. Extrapolate Σ to Δt → 0 and compare the extrapolated total with the true entropy production; if the extrapolated value differs systematically from the true value, or if the 5 ms measurement exceeds the true value (as the inset shows it can), then the finite-resolution protocol does not measure entropy production directly and any ranking of conditions would need a Δt-dependent correction.","supporting_citations":[],"review_version":1}