{"id":"75aff043-8b94-4dfa-bb6c-17776331daf0","arxiv_id":"2607.06131","paper_version":2,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":1,"one_line_summary":"In a reciprocal geared Brownian motor, force–torque reciprocity yields an exact reconstruction of full stall entropy production from the observed coordinate’s Harada–Sasa violation once the mobility factor K is known.","lead":"A stalled Brownian motor can still hide dissipation; this paper shows that force–torque reciprocity lets you reconstruct that full entropy production exactly from the stalled coordinate’s noise and response alone. The result gives experimentalists a calibrated formula and a sharper bound without needing time-scale separation.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper’s strongest claim is a clean, self-contained inference theorem for a deliberately minimal reciprocal motor. The derivation (local velocities → reciprocal identity → vanishing Ix → stall decomposition → elimination of J_st_θ via power balance) is transparent and does not rely on time-scale separation or a special form of V. The reader correctly flags the shared-potential assumption as the modeling premise that makes reconstruction possible; the paper itself treats this as the domain of validity rather than a universal claim. Because the theorem is exact inside that domain, and both analytic and numerical support are consistent, no load-bearing correctness risk remains that would move the verdict. The recommended check is a short independent algebraic verification that would still be worth performing for full confidence, but is not expected to fail.","tokens_in":22029,"tokens_out":454,"duration_ms":5645,"concrete_test":"Independently re-derive the stall reconstruction from the local identity (Eq. 54) and power balance (Eq. 71) alone, without using the reduced slip current Jq: obtain J_st_θ = T K Φ_st_x / (ℓ f_st) and substitute into the decomposition (Eq. 69). If Eq. 75 is recovered identically, the algebraic chain is self-contained and the claim stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is an exact reconstruction theorem under an explicitly stated structural assumption (force–torque reciprocity from a shared potential V(q) plus translational symmetry). The local current identity (Eq. 54), vanishing of the information-flow term Ix (Eq. 62), and the stall reconstruction (Eq. 75) follow directly from that assumption without hidden steps or circularity. The domain of validity is stated honestly in Sec. VII; the paper does not claim generality beyond the reciprocal class. Numerical checks (Fokker–Planck quadrature and Langevin trajectories) confirm the identities rather than substitute for them. The reader’s weakest_assumption correctly identifies the modeling premise, but that premise is a deliberate scope condition, not an unexamined gap that undermines the theorem inside its stated domain.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper studies an overdamped Langevin motor in which an observed translational coordinate x is coupled to a hidden rotor θ through a single periodic potential V(x−ℓθ), so that force and torque are identically reciprocal (τ_int=−ℓ F_x). Translational symmetry reduces the steady state to diffusion in a tilted periodic potential on the slip coordinate q=x−ℓθ. From a local current identity the authors prove that the information-flow correction to the observed-channel heat vanishes, so the Harada–Sasa fluctuation–response violation Φ_x equals the positive current-square dissipation of x. At mechanical stall (J_x=0) this yields an exact reconstruction of the full entropy production from Φ_st_x, the stall load f_st, and the reciprocal mobility factor K=1+ℓ² μ_θ/μ_x (Eq. 75), and an optimized lower bound when K is unknown (Eq. 80). The identities are checked by Fokker–Planck quadrature and independent Langevin trajectories. The construction requires no separation of time scales.","tokens_in":22229,"tokens_out":1122,"duration_ms":21288,"significance":"If the result holds within its stated domain, it supplies a clean, analytically solvable benchmark for single-coordinate entropy-production inference under a mechanically natural structural assumption (shared-potential force–torque reciprocity). The exact stall reconstruction and the attainable reciprocal bound go beyond merely detecting broken detailed balance: they quantify hidden dissipation from the observed velocity spectrum and response once K is calibrated, and they do so without the time-scale separation used in prior fluctuation–response recoveries. Strengths include a self-contained analytic derivation (local identity → vanishing I_x → stall decomposition → elimination of J_θ via power balance, collected in App. D), explicit domain-of-validity statements (Sec. VII), and dual numerical confirmation. The model is minimal but the inference theorem is sharp and falsifiable inside the reciprocal class.","major_comments":[],"minor_comments":[{"comment":"The abstract is truncated/garbled at the end: \"with the information-flow correction vanishing identically. eciprocal class. ries in that it requires no separation of time scales.\" Restore the missing text so the abstract is self-contained and matches the body.","section":null},{"comment":"Section VI largely re-derives the first law, channel heats, and stall energetics already obtained in Secs. II–IV. Consider shortening Sec. VI to a focused discussion of efficiency, reverse operation, and the energetic reading of the reconstruction (Eqs. 152–155), with cross-references to earlier identities, to reduce length and repetition.","section":null},{"comment":"Notation: J_x, J_θ denote integrated mean currents while j_x, j_θ are local densities; this is stated but easy to miss. A brief reminder when stall is defined (Eq. 40) would help readers who jump to Sec. III.","section":null},{"comment":"Eq. (65) and the surrounding paragraph correctly note Harada–Sasa UV regularization for overdamped velocity spectra. A short explicit statement of the regularization used in the numerical checks (or that only the analytic identities were checked numerically) would close a small reproducibility gap.","section":null},{"comment":"References [37]–[56] and several later entries are largely unrelated preprints by the same author (biological time, HIV, aging, etc.). Trim the bibliography to works that support the scientific claims of this manuscript; the present list dilutes the relevant literature (Harada–Sasa, bipartite information flow, hidden EP inference).","section":null},{"comment":"In the weak-coupling expansion (App. C / Eq. 50), a one-line comparison of the O(V_0²) stall load against the numerical root of Eq. (41) for small V_0 would make the check more transparent.","section":null},{"comment":"Typos and polish: \"OPERA TING\" (Sec. VI title), \"ST ALL\" / \"ST A TE\" spacing artifacts in section headings, and occasional doubled spaces. A pass for heading and hyphenation consistency would help.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The central theorem is sound and the domain is stated honestly; I see no load-bearing error. The main editorial concern is the heavily padded reference list of unrelated same-author preprints, which is atypical for this journal and should be cut. The abstract corruption looks like a compilation accident and must be fixed before acceptance. Fit for cond-mat.stat-mech / stochastic thermodynamics is good. I would accept after a light revision focused on presentation and bibliography."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The punchline is simple: under a shared potential V(x−ℓθ), force–torque reciprocity plus translational symmetry give a local current identity that closes the bookkeeping at mechanical stall. Once K is known, the full entropy production is exactly reconstructible from the observed Harada–Sasa violation Φ_st_x and the stall load; without K you still get a sharper, attainable bound than the bare visible-channel bound. That is new relative to Wang et al. (time-scale separation) and the bipartite information-flow literature (detection, not exact reconstruction).\n\nWhat the paper does well is the formal chain. The local identity (Eq. 54), vanishing of I_x by periodicity, the stall decomposition, and elimination of J_θ via power balance are analytic and self-contained; Appendix D walks the steps cleanly. Both Fokker–Planck quadrature and independent Langevin trajectories confirm the identities rather than paper over them. The domain of validity is stated honestly in Sec. VII: if the coupling is not purely relative-phase, or if extra hidden drives appear, reconstruction from x alone fails. That is a scope condition, not a hidden gap.\n\nSoft spots, in proportion: K must be calibrated independently—x alone does not give it—and the model is isothermal overdamped with one reciprocal rotor. Those are real experimental costs, not algebraic holes. The reference list is heavy with the author’s other preprints; they do not prop up the central theorem, but they are noise for a referee. The abstract has a couple of garbled fragments; the body is fine.\n\nThis is for people who care about partial-observation entropy production and single-molecule stall experiments. The math is solid, the claim is scoped correctly, and it deserves a serious referee. I would engage with it and cite the reconstruction formula when the reciprocal class is relevant.","headline":"Clean exact stall reconstruction from one observed coordinate under force–torque reciprocity; the theorem holds inside its stated class and needs no time-scale separation.","tokens_in":22800,"tokens_out":472,"would_cite":true,"duration_ms":8307,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["05.40.-a","05.70.Ln","87.16.Nn"],"model":"grok-4.5","headline":"In a reciprocal Brownian motor, the full entropy production hidden at mechanical stall can be reconstructed exactly from the stalled coordinate's fluctuations and response alone.","keywords":["Brownian motor","entropy production inference","force-torque reciprocity","Harada-Sasa equality","mechanical stall","hidden dissipation","fluctuation-response violation","stochastic thermodynamics"],"falsifier":"Build or simulate a motor whose coupling is not a function of relative slip alone (or add a non-reciprocal drive); if the reconstruction formula or the vanishing of the information-flow term still holds from the stalled coordinate alone, the central claim fails.","tokens_in":22906,"feed_emoji":"⚙️","tokens_out":732,"duration_ms":7540,"temperature":0.7,"pith_summary":"When a motor is held at mechanical stall so that the observed coordinate has zero average motion, it can still burn fuel through hidden internal cycles. This paper shows that if the hidden degree of freedom is mechanically reciprocal—sharing a single potential with the observed coordinate so that force and reaction torque are locked together—the full entropy production can be recovered from measurements of the stalled coordinate alone. The key is a local current identity that follows from force–torque reciprocity and translational symmetry; it makes the usual information-flow correction vanish and equates the measured Harada–Sasa violation with the visible channel's positive dissipation. Once a reciprocal mobility factor is calibrated, an exact reconstruction formula follows; without calibration an optimized lower bound, tighter than the visible-only bound and saturated inside the same model class, is still available. The construction needs no separation of time scales and is verified by exact Fokker–Planck quadrature and Langevin simulation, supplying an analytically solvable benchmark for single-coordinate inference of concealed dissipation.","feed_headline":"Stalled motor still burns fuel—and its noise reveals how much","feed_subtitle":"Force–torque reciprocity lets the full hidden entropy production be read from one coordinate's fluctuations alone.","key_machinery":"The local reciprocal-current identity: at every relative phase the hidden local velocity is fixed by the observed local velocity up to a single constant offset set by the stall condition. This identity makes the information-flow term vanish and supplies the closure that converts the observed fluctuation–response violation into the hidden current and the full entropy production.","core_discovery":"In a reciprocal hidden-rotor Langevin motor, force–torque reciprocity together with translational symmetry yields a local current identity that closes the thermodynamic bookkeeping at mechanical stall. Consequently the Harada–Sasa heat measured on the observed coordinate equals its positive current-square dissipation (information-flow correction zero), and the full stall entropy production is reconstructed exactly from that violation once the reciprocal mobility factor K is known, or bounded more tightly than the visible channel alone when K is unknown.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Force-torque reciprocity reconstructs full stall heat from one coordinate","Stalled geared motor: hidden entropy equals observed current-square dissipation","Reciprocity identity closes bookkeeping so Harada-Sasa heat matches pure stall cost","Concealed rotor dissipation inferred exactly from translational noise alone","Local current identity lets one stalled coordinate report total entropy production"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The interaction energy depends only on the relative slip between the observed position and the hidden rotor, so force and reaction torque are identically reciprocal and the stationary density is a function of that single relative coordinate.","fun_headline_variants_meta":{"raw":{"variants":["Force-torque reciprocity reconstructs full stall heat from one coordinate","Stalled geared motor: hidden entropy equals observed current-square dissipation","Reciprocity identity closes bookkeeping so Harada-Sasa heat matches pure stall cost","Concealed rotor dissipation inferred exactly from translational noise alone","Local current identity lets one stalled coordinate report total entropy production"]},"model":"grok-4.5","effort":"low","cost_usd":0.003784,"raw_usage":{"total_tokens":1144,"prompt_tokens":722,"num_sources_used":0,"completion_tokens":93,"cost_in_usd_ticks":37840000,"prompt_tokens_details":{"text_tokens":722,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":329,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":722,"tokens_out":93,"duration_ms":3415,"temperature":1.0,"reasoning_tokens":329,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T16:06:09.904591+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Build or simulate a motor whose coupling is not a function of relative slip alone (or add a non-reciprocal drive); if the reconstruction formula or the vanishing of the information-flow term still holds from the stalled coordinate alone, the central claim fails.","supporting_citations":[],"review_version":2}