{"id":"847811aa-bbd8-4ec0-8258-cd274d1f48b2","arxiv_id":"2604.02914","paper_version":2,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"Non-Galilean Hamiltonian flocks obey a generalized time-reversal symmetry that produces a mixed position-polarity FDT, Onsager-Casimir reciprocity, nontrivial angular diffusion, and zero true entropy production.","lead":"Hamiltonian flocks, which look like active matter but are fully conservative, obey a generalized time-reversal symmetry that mixes position and polarity. This yields a mixed fluctuation-dissipation theorem and shows that naive entropy-production estimates can be spurious.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The central claim is that a known conservative non-Galilean model obeys a generalized TRS that produces a mixed FDT, Onsager-Casimir relations, and identically zero entropy production, while the naïve TRS yields a spurious production rate. The derivation is self-contained: the Langevin equations are justified from an explicit bath (App. A), the action symmetry is verified term-by-term (App. B.2), the four FDT relations and the Casimir sign flip follow by Noether (App. B.3), and the entropy-production calculation cancels exactly under the generalized map (App. B.5) but not under the incomplete one (App. B.6). Numerical checks of MSDs, MSADs, and response functions are consistent with the analytic predictions. The modeling assumption flagged by the reader is therefore the only plausible soft spot, yet it is already supported by two independent bath constructions and by the recovery of the correct equilibrium measure. No further load-bearing concern surfaces. The reader's ACCEPT / high-confidence verdict therefore stands.","tokens_in":23093,"tokens_out":602,"duration_ms":5002,"concrete_test":"Independently recompute the single-particle angular diffusion constant D_R from the long-time MSAD of the underdamped Langevin equations (3)-(6) at v_0=0 for a few values of eta K^{2} (e.g., 0,1,4) and compare against the closed-form prediction D_R=k_BT/(\theta_r+K^{2}/\theta_t) of Appendix C; agreement within sampling error confirms that the bath and the FDT-derived mobility are consistent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest assumption (that the Zwanzig-Mori-derived Langevin bath with white-noise limit correctly realizes the tachostat-augmented canonical measure) is the natural soft spot, but the paper already closes it carefully. Appendix A derives the friction/noise from two independent linear couplings (angles and spins) and shows both collapse to the same white-noise Langevin equations (3)-(4). Appendix B.2 then verifies that the MSRJD action is invariant under the generalized TRS (r_t\to r_{-t}, \theta_t\to\theta_{-t}+\theta, v_0\to-v_0) and that the initial-condition term recovers exactly the canonical weight e^{-eta(H-v_0·P)}. The same transformation yields vanishing entropy production (B.82) while the naïve (spin-preserving) reversal produces a spurious nonzero rate. Once that construction is granted, the mixed FDT, Onsager-Casimir reciprocity, and the cautionary message about active-matter diagnostics follow algebraically. No internal inconsistency or unsupported leap appears.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper studies Hamiltonian flocks: conservative, non-Galilean polar liquids with spin-velocity coupling K that can exhibit collective motion without activity. After deriving Langevin dynamics (with a tachostat fixing center-of-mass velocity v0) via a Zwanzig-Mori construction, the authors construct the MSRJD action and show it is invariant under a generalized time-reversal map that reverses positions, flips spins (theta to theta+pi), and reverses v0. This symmetry yields mixed fluctuation-dissipation relations Ra,b(tau)=-beta partial_tau C^c_a,b(tau) for a,b in {r,s}, Onsager-Casimir reciprocity (because spin is odd under T), vanishing entropy production under the correct reversal, and a spurious nonzero production rate under the naive spin-preserving reversal. Angular dynamics are shown to be rich, with an effective long-time rotational diffusion constant and Kramers-type confinement when Kv0 is nonzero. Analytic predictions for MSDs/MSADs and overdamped limits are checked against single-particle Langevin simulations.","tokens_in":23381,"tokens_out":740,"duration_ms":6547,"significance":"If correct, the work supplies a clean equilibrium baseline for systems that look active because they break Galilean invariance. The mixed FDT, Onsager-Casimir relations, and the explicit demonstration that naive TRS produces a spurious entropy production rate are concrete, falsifiable diagnostics that active-matter studies can use when only partial observables are available. Strengths include the fully explicit path-integral construction (Appendices B.2-B.6), the dual Zwanzig-Mori derivations that both collapse to the same white-noise Langevin equations, closed-form MSAD expressions (including the self-consistent DR and the Kramers picture), and direct numerical checks of the FDT and angular diffusion. The cautionary message about mis-diagnosing distance to equilibrium is timely and well-supported by the calculation.","major_comments":[],"minor_comments":[{"comment":"Figures 1-3 and 6-7 would benefit from explicit parameter boxes (beta, K, v0, gamma) in every panel; some insets are hard to read at print size.","section":null},{"comment":"Notation for the co-moving connected correlator C^c is introduced late; a short definition table or early equation would help readers who jump to the FDT summary.","section":null},{"comment":"Appendix C's recursive expansion for DR is useful; a short numerical comparison of D^(0)_R versus the fully self-consistent root for a few kappa values would make the validity range more transparent.","section":null},{"comment":"A few typos remain (e.g., 'time-reveralsymmetry', 'na\\\"ive' spacing, and occasional missing spaces around equations). A light copy-edit pass would clean them.","section":null},{"comment":"The discussion of possible mappings of active systems onto higher-dimensional non-Galilean Hamiltonians is intriguing but brief; one or two concrete pointers to existing non-reciprocal-to-Hamiltonian constructions would strengthen the outlook.","section":null}],"recommendation":"accept","confidential_remarks":"The manuscript is long and appendix-heavy, but the central claims are load-bearing and carefully derived. Fit for a statistical-mechanics journal is excellent; no novelty or citation concerns. I see no reason to request major changes."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing to know is that this paper takes the already-known conservative non-Galilean flock model and shows it is invariant under a generalized time-reversal map (positions reverse, spins flip, bath velocity reverses). That map produces a mixed position-polarity FDT, Onsager-Casimir reciprocity rather than ordinary Onsager, a non-trivial long-time angular diffusion constant, and identically zero entropy production. The naïve spin-preserving reversal yields a spurious nonzero rate that people could misread as a distance to equilibrium.\n\nWhat is new is exactly that package. Prior Hamiltonian-flock papers established the equilibrium measure and the flocking phenomenology; they did not derive the dynamical symmetries or the cautionary entropy-production result. The appendices do the work carefully: Zwanzig-Mori construction of the Langevin bath (two independent linear couplings both collapse to the same white-noise equations), MSRJD action, explicit invariance under the generalized map, extraction of the four FDT relations, vanishing of the Onsager-Machlup production, and the spurious-production calculation under incomplete reversal. Angular dynamics (effective DR, Kramers-like confinement when Kv0 \neq 0) are worked out and checked numerically. The math is transparent and the citation pattern is honest.\n\nThe soft spot is the modeling assumption that this particular friction/noise realizes the tachostat-augmented canonical ensemble. The paper closes it as well as one can: Appendix A derives the terms, Appendix B.2 verifies that the initial-condition piece recovers e^{-eta(H-v0·P)} and that the action is invariant. Once that construction is granted, everything else is algebraic. No internal contradiction, no free parameters tuned to force the FDT, no load-bearing fitting. Single-particle numerics are illustrative rather than exhaustive, but they are not asked to carry the central claim.\n\nThis is for people who measure FDT violations or entropy production in polar active systems and for anyone who wants a clean equilibrium baseline that still looks active. It deserves a serious referee. I would accept it for peer review and I would cite the mixed FDT and the spurious-production warning.","headline":"Clean derivation of generalized TRS for Hamiltonian flocks: mixed FDT, Onsager-Casimir, and a concrete warning that naïve entropy production is spurious.","tokens_in":23939,"tokens_out":520,"would_cite":true,"duration_ms":5853,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Hamiltonian flocks obey a generalized time-reversal symmetry that yields a mixed position-polarity fluctuation-dissipation theorem and zero entropy production.","keywords":["Hamiltonian flocks","time-reversal symmetry","fluctuation-dissipation theorem","Onsager-Casimir reciprocity","entropy production","non-Galilean dynamics","polar liquids","active matter"],"falsifier":"Compute the entropy-production rate from the ratio of forward and reverse path probabilities under the spin-flipping map; if the rate is nonzero, or if the mixed position-spin FDT fails in the co-moving frame, the claimed generalized symmetry is false.","tokens_in":23990,"feed_emoji":"🔄","tokens_out":933,"duration_ms":8884,"temperature":0.7,"pith_summary":"Hamiltonian flocks are conservative, non-Galilean models of polar liquids that can form moving clusters without any active driving. This paper shows that they still obey a generalized time-reversal symmetry: positions reverse, spins flip sign, and the bath velocity reverses. That symmetry produces a fluctuation-dissipation theorem that mixes position and polarity degrees of freedom, enforces Onsager-Casimir reciprocity rather than ordinary Onsager relations, and implies identically zero entropy production. Using the ordinary time-reversal operation that leaves spins unchanged generates a spurious nonzero entropy-production rate that would be misread as a distance from equilibrium. The same coupling also produces nontrivial long-time angular diffusion and Kramers-like barrier crossings when a global velocity is present. The result supplies a concrete warning for active-matter studies: apparent irreversibility can be an artifact of choosing the wrong reversal, and looking for hidden extensions of time-reversal symmetry may recover equilibrium structure where none was expected.","feed_headline":"Flocks without activity still obey a hidden time-reversal law","feed_subtitle":"Spin flip restores the fluctuation-dissipation theorem and zeros the entropy production that naïve reversal would invent","key_machinery":"The generalized time-reversal map T (r_t → r_−t, θ_t → θ_−t + π so s → −s, v_0 → −v_0) that leaves the Martin-Siggia-Rose-Janssen-De Dominicis action of the Langevin dynamics invariant and thereby generates the mixed FDT and zero entropy production.","core_discovery":"The model is invariant under the generalized time reversal that sends positions to their time-reversed counterparts, spins to their negatives, and the imposed bath velocity to its negative. That invariance leaves the dynamical action unchanged, yields the connected FDT relating every pair of position and spin correlators and responses, produces Onsager-Casimir reciprocity because spin is odd, and forces the entropy production rate to vanish identically. The naïve reversal that keeps spins unchanged produces a nonzero spurious production rate.","pith_inferences":["The same construction may allow classes of active polar models to be rewritten as higher-dimensional non-Galilean Hamiltonian systems, giving access to equilibrium sampling tools.","Experimental estimates of extractable work in living or synthetic active matter could change once hidden polarity degrees of freedom are restored to the time-reversal map.","The overdamped limit with a tachostat still preserves the Boltzmann measure for the angles, so the mixed FDT survives even when inertia is dropped."],"forward_implications":["Position mean-square displacements obey the ordinary Einstein relation once displacements are measured in the frame moving at the bath velocity.","Long-time angular diffusion is controlled by an effective friction that depends on the spin-velocity coupling K, not the bare rotational friction alone.","When a nonzero global velocity is present the spins feel an effective confining potential and exhibit Kramers barrier-crossing dynamics before diffusing.","Entropy-production measurements that ignore spin-oddness under time reversal will report a false distance from equilibrium.","Any polar system whose Galilean invariance is broken may admit an analogous generalized reversal that restores an equilibrium FDT."],"fun_headline_variants":["Hamiltonian flocks hide a spin-flipping time-reversal symmetry","Spin-odd TRS yields mixed FDT in activity-free flocks","Generalized reversal zeros entropy in Hamiltonian polar liquids","True spin-flip symmetry restores FDT and kills false entropy","Naïve TRS invents entropy; spin reversal restores equilibrium laws"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The friction and noise terms obtained from the linear bath-oscillator construction correctly realize the canonical ensemble that also fixes the center-of-mass velocity.","fun_headline_variants_meta":{"raw":{"variants":["Hamiltonian flocks hide a spin-flipping time-reversal symmetry","Spin-odd TRS yields mixed FDT in activity-free flocks","Generalized reversal zeros entropy in Hamiltonian polar liquids","True spin-flip symmetry restores FDT and kills false entropy","Naïve TRS invents entropy; spin reversal restores equilibrium laws"]},"model":"grok-4.5","effort":"low","cost_usd":0.006454,"raw_usage":{"total_tokens":1663,"prompt_tokens":785,"num_sources_used":0,"completion_tokens":90,"cost_in_usd_ticks":64540000,"prompt_tokens_details":{"text_tokens":785,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":788,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":785,"tokens_out":90,"duration_ms":6509,"temperature":1.0,"reasoning_tokens":788,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-13T13:40:32.278131+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Compute the entropy-production rate from the ratio of forward and reverse path probabilities under the spin-flipping map; if the rate is nonzero, or if the mixed position-spin FDT fails in the co-moving frame, the claimed generalized symmetry is false.","supporting_citations":[],"review_version":2}