{"id":"00f665c8-3951-4c8f-ba10-9c89c2459019","arxiv_id":"2606.19702","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A parity selection rule forbids equalities between mutual information and entropy production in rotation-driven linear nonequilibrium steady states when relaxation and diffusion matrices commute.","lead":"The paper identifies a parity selection rule forbidding tight equalities between symmetric information and entropy production in certain driven steady states. A smart generalist might read it to understand new constraints on information-dissipation tradeoffs in nonequilibrium systems and a proposed experimental test.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Claim that parity rule survives isotropic stable noise (α<2) rests on unverified extension of symmetry argument beyond Gaussian case","rationale":"Reader correctly flags the stable-noise extension as weakest assumption; my concern is the same point but made concrete on the entropy definition. Full-text derivation (if present) would need to be checked against the proposed simulation; passing the test would support the claim, failure would require restricting to Gaussian noise.","tokens_in":1671,"tokens_out":330,"duration_ms":29567,"concrete_test":"Numerically integrate the 2D linear SDE with commuting matrices and isotropic α-stable increments (α=1.5) for drive strength λ and -λ; estimate I(X_t; X_{t+τ}) via k-NN or kernel methods on long trajectories and test whether the two values agree within bootstrap error; repeat for α=2 (Gaussian) as control.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that rotational symmetry of the drift alone forces snapshot mutual information to be exactly even under drive reversal (when relaxation and diffusion commute), and that this holds for heavy-tailed isotropic stable noise. Differential entropy and mutual information for multivariate α-stable laws lack the explicit quadratic forms used in the Gaussian OU derivation; the characteristic-function evolution under linear drift may not preserve the required even/odd decomposition without additional structure on the Lévy measure. This is the least secure step because the abstract asserts survival while the commutativity condition is stated separately, leaving open whether isotropy plus rotational drift suffices for the parity when variance is infinite.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims a parity selection rule for snapshot mutual information and entropy production in rotation-driven linear nonequilibrium steady states. When the relaxation and diffusion matrices commute, mutual information between time slices is exactly even under drive reversal, with parity violation linear in the commutator norm. Full isotropy yields drive-independent mutual information (closed-form planar value ~0.145 nats). Entropy production is quadratic in the drive with an explicit prefactor in traces and determinant. Even/odd sector orthogonality implies one-sided thermodynamic uncertainty bounds. The rule is asserted to rest solely on rotational drift symmetry and to survive isotropic α-stable noise (α<2), with a proposed falsifiable test on an augmented electrical Brownian gyrator.","tokens_in":1799,"tokens_out":550,"duration_ms":22070,"significance":"If the central symmetry argument holds, the result supplies a parameter-free constraint explaining the absence of tight symmetric-information/entropy-production equalities, furnishes closed-form expressions, and extends information-dissipation relations to infinite-variance regimes where conventional bounds fail. The proposed circuit-level test adds direct falsifiability.","major_comments":[{"comment":"Abstract (stable-noise claim): the assertion that rotational symmetry of the drift alone forces the snapshot mutual information to remain exactly even under drive reversal for isotropic α-stable noise (α<2) is load-bearing for the claim that the rule survives where variance-based bounds are vacuous. Differential entropy and mutual information for multivariate stable laws lack the quadratic forms of the Gaussian OU case; the characteristic-function evolution under linear drift must be shown explicitly to preserve the required even/odd decomposition without further restrictions on the Lévy measure. The commutativity condition is stated separately, leaving open whether isotropy plus rotational drift suffices.","section":"Abstract (stable-noise extension)"},{"comment":"Abstract (planar MI value): the stated closed-form planar mutual information of about 0.145 nats under full isotropy should be accompanied by the explicit expression or derivation (in terms of matrix traces/determinant or the even-sector integral) so that the numerical value can be verified independently.","section":"Abstract (planar mutual information)"}],"minor_comments":[{"comment":"The phrase 'about 0.145 nats' would benefit from additional digits or an exact symbolic form if the derivation yields one.","section":"Abstract"},{"comment":"Notation for the relaxation and diffusion matrices should be introduced with a brief reminder of their dimensions and symmetry properties at first use.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and the constructive major comments. We address each point below and will incorporate the requested clarifications in a revised manuscript.","responses":[{"response":"We agree that an explicit derivation via the characteristic function is needed to substantiate the claim for α-stable noise. The rotational symmetry of the drift combined with isotropy of the Lévy measure ensures that the log-characteristic function decomposes into even and odd sectors under drive reversal, with the linear drift term preserving this parity because it acts as a rotation in the Fourier domain. In the revision we will add a dedicated appendix deriving the time evolution of the characteristic function for the linear SDE driven by isotropic α-stable noise, confirming that no further restrictions on the Lévy measure are required beyond isotropy. This will make the extension fully rigorous.","revision_made":"yes","referee_comment":"[Abstract (stable-noise extension)] Abstract (stable-noise claim): the assertion that rotational symmetry of the drift alone forces the snapshot mutual information to remain exactly even under drive reversal for isotropic α-stable noise (α<2) is load-bearing for the claim that the rule survives where variance-based bounds are vacuous. Differential entropy and mutual information for multivariate stable laws lack the quadratic forms of the Gaussian OU case; the characteristic-function evolution under linear drift must be shown explicitly to preserve the required even/odd decomposition without further restrictions on the Lévy measure. The commutativity condition is stated separately, leaving open whether isotropy plus rotational drift suffices."},{"response":"We accept the suggestion. The value 0.145 nats is obtained by evaluating the even-sector integral of the mutual information expression under full isotropy (equal eigenvalues of the relaxation matrix and proportional diffusion matrix), which reduces to a closed-form combination of traces and the determinant. In the revised manuscript we will state the explicit integral expression (or its evaluated result) either in the abstract or immediately following the numerical value in the main text, allowing independent verification.","revision_made":"yes","referee_comment":"[Abstract (planar mutual information)] Abstract (planar MI value): the stated closed-form planar mutual information of about 0.145 nats under full isotropy should be accompanied by the explicit expression or derivation (in terms of matrix traces/determinant or the even-sector integral) so that the numerical value can be verified independently."}],"tokens_in":1416,"tokens_out":510,"duration_ms":20704,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's main result is a parity selection rule that forces snapshot mutual information between time slices to be exactly even under drive reversal in rotation-driven linear nonequilibrium steady states, provided the relaxation and diffusion matrices commute. Full isotropy then makes the information drive-independent, with a specific planar value around 0.145 nats, while entropy production stays quadratic in the drive with an explicit prefactor.\n\nThe work supplies closed-form expressions and shows how even-odd orthogonality restricts thermodynamic uncertainty relations to one-sided bounds. The rotational symmetry of the drift is the key assumption, and the paper extends the claim to isotropic stable noise with tail index below two, where variance-based bounds fail. It also outlines a concrete falsifiable test using an electrical Brownian gyrator with independent drive control and circuit-level stable-noise injection.\n\nThe stable-noise extension is the softest part. Differential entropy and mutual information for multivariate α-stable laws lack the simple quadratic structure of the Gaussian case, and the characteristic-function evolution under linear drift may not automatically preserve the required even-odd split without further conditions on the Lévy measure. The abstract separates the commutativity condition, so it is not obvious that isotropy plus rotational drift alone suffices when variance is infinite.\n\nThis is for researchers working on symmetry constraints and exact relations in stochastic thermodynamics, especially linear driven systems. Readers who want explicit formulas rather than general inequalities will find the derivations and the proposed experiment useful.\n\nIt deserves peer review because the claims are specific and checkable. Send it out, but ask referees to examine the characteristic-function argument for the α-stable case in detail.","headline":"The parity selection rule for even mutual information under drive reversal in commuting linear systems is the main new claim, with closed forms and a proposed test, though the stable-noise extension is the least secure step.","tokens_in":2264,"tokens_out":408,"would_cite":false,"duration_ms":11192,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Snapshot mutual information is exactly even under drive reversal when relaxation and diffusion matrices commute in linear nonequilibrium steady states.","keywords":["parity selection rule","snapshot mutual information","entropy production","drive reversal","nonequilibrium steady states","rotational symmetry","stable noise","Brownian gyrator"],"falsifier":"Measuring a nonzero odd component in the snapshot mutual information under drive reversal for a system with commuting matrices would falsify the parity selection rule.","tokens_in":2576,"feed_emoji":"","tokens_out":533,"duration_ms":15941,"temperature":0.7,"pith_summary":"The paper shows that a parity selection rule forbids tight equalities between symmetric information and entropy production in rotation-driven linear nonequilibrium steady states. When the relaxation and diffusion matrices commute, the snapshot mutual information between two time slices remains exactly even if the drive direction is reversed. Breaking commutativity introduces parity violation that grows linearly with the commutator norm. In the isotropic case this yields a drive-independent mutual information of about 0.145 nats, while entropy production stays exactly quadratic in the drive amplitude with a closed-form prefactor. The selection rule depends only on rotational symmetry of the drift and continues to hold for heavy-tailed isotropic stable noise.","feed_headline":"Mutual information stays even under drive reversal in steady states","feed_subtitle":"Commuting matrices enforce parity in information while dissipation remains quadratic in drive for rotation-driven systems.","key_machinery":"The parity selection rule arising from rotational symmetry of the drift under drive reversal, which separates even and odd sectors in the information and dissipation quantities.","core_discovery":"For rotation-driven linear nonequilibrium steady states with commuting relaxation and diffusion matrices, the snapshot mutual information between time slices is exactly even under drive reversal by a parity selection rule originating from the rotational symmetry of the drift. Entropy production is quadratic in the drive, and the rule extends to heavy-tailed stable noise.","pith_inferences":["The selection rule may provide a general principle for separating information contributions in other driven systems.","Experimental verification using modified Brownian gyrators could test the rule's robustness beyond Gaussian noise.","This parity property could inform design of information engines that exploit even-odd separation.","Connections to symmetry-based bounds in stochastic thermodynamics."],"forward_implications":["The mutual information remains even under drive reversal.","Entropy production is quadratic in drive with explicit prefactor from traces and determinant.","Thermodynamic uncertainty bounds are one-sided due to orthogonality of sectors.","The result holds for isotropic stable noise with tail index below two.","In planar isotropic case, mutual information is drive-independent at 0.145 nats."],"fun_headline_variants":["Parity rule makes mutual info even under drive reversal","Commuting matrices enforce even info in rotation-driven states","Drive reversal leaves snapshot info even in steady states","Entropy production quadratic in drive for aligned matrix systems","Parity selection governs information parity in nonequilibrium states"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The load-bearing premise is that the drift possesses exact rotational symmetry, without which the parity selection rule would not hold.","fun_headline_variants_meta":{"raw":{"variants":["Parity rule makes mutual info even under drive reversal","Commuting matrices enforce even info in rotation-driven states","Drive reversal leaves snapshot info even in steady states","Entropy production quadratic in drive for aligned matrix systems","Parity selection governs information parity in nonequilibrium states"]},"model":"grok-4.3","cost_usd":0.00452,"raw_usage":{"total_tokens":2223,"prompt_tokens":615,"num_sources_used":0,"completion_tokens":73,"cost_in_usd_ticks":45199500,"prompt_tokens_details":{"text_tokens":615,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1535,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":615,"tokens_out":73,"duration_ms":9089,"temperature":1.0,"reasoning_tokens":1535,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T15:49:06.981163+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Measuring a nonzero odd component in the snapshot mutual information under drive reversal for a system with commuting matrices would falsify the parity selection rule.","supporting_citations":[],"review_version":1}