{ "schemaVersion": "1.6", "slug": "fixed-correlations-weak-dissipation", "title": "Fixed time-asymmetric correlations with arbitrarily weak dissipation", "shortTitle": "Same correlations, any dissipation", "url": "https://evidencepress.org/releases/fixed-correlations-weak-dissipation/", "oneLine": "One fixed time-asymmetric covariance is shared by Markov models with every positive entropy-production rate, so its Gaussian value, 1/3, is not the lower bound on dissipation that Seara, Machta and Murrell (2021) stated for nonlinear systems.", "abstract": "Experiments often estimate how much energy a living or driven system dissipates from the time asymmetry of its measured correlations. A popular shortcut assigns the observed covariance the entropy-production rate of a Gaussian process with the same covariance, and Seara, Machta and Murrell (Nature Communications 12, 392, 2021) stated that this gives a lower bound for nonlinear systems as well. This candidate shows that it does not. A family of fully observed four-state Markov chains shares one fixed, nonzero, time-asymmetric covariance at every lag, with bounded transition rates and uniform mixing, while their entropy-production rates take every positive value. Fully observed planar Markov diffusions with linear drift and state-dependent noise have exactly the same covariance, with entropy-production rates filling (0, 1/3], where 1/3 is the Gaussian value; a Student-type member has rate α/(3(α+1)). In both cases rare, large excursions carry the covariance. A reversible-gating construction gives the general mechanism, the paper locates the missing step in the published justification, and an established fourth-order bound recovers up to 93.5% of the exact rate on the example. Weak dissipation at fixed covariance needs growing amplitudes or heavy-tailed noise, and diffusions with constant noise remain open. AI-assisted, unrefereed candidate; no external peer review, independent reproduction or formal verification is claimed.", "datePublished": "2026-10-28", "dateModified": "2026-10-28", "version": "1.0.0-candidate", "doi": "10.5281/zenodo.23721112", "doiUrl": "https://doi.org/10.5281/zenodo.23721112", "conceptDoi": "10.5281/zenodo.23721111", "pdfUrl": "https://github.com/ipitchford/fixed-correlations-weak-dissipation/releases/download/v1.0.0-candidate/fixed-correlations-weak-dissipation-1.0.0-candidate.pdf", "altPdfUrl": null, "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23721112", "repoUrl": "https://github.com/ipitchford/fixed-correlations-weak-dissipation", "releaseUrl": "https://github.com/ipitchford/fixed-correlations-weak-dissipation/releases/tag/v1.0.0-candidate", "markdownUrl": "https://evidencepress.org/releases/fixed-correlations-weak-dissipation/index.md", "bibtexUrl": "https://evidencepress.org/releases/fixed-correlations-weak-dissipation/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/fixed-correlations-weak-dissipation.mp3", "imageUrl": "https://evidencepress.org/assets/og/fixed-correlations-weak-dissipation.png?v=9a1e73faec", "coverArtUrl": "https://evidencepress.org/assets/art/fixed-correlations-weak-dissipation.svg?v=2ebf2d7101", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/fixed-correlations-weak-dissipation.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/fixed-correlations-weak-dissipation.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed AI-assisted candidate. Every theorem has a written proof supported by exact, symbolic and numerical checks; the kurtosis probe and Table 1 are numerical and labelled as such. Internal AI-assisted review only, including two adversarial audits by a different model and a targeted proof audit. External specialist review, independent reproduction and formal verification have not been established." }, "assurance": [ { "dimension": "availability", "label": "Availability and archiving", "question": "Is the evidence package publicly retrievable from an archive under a persistent identifier?", "state": "passed", "evidenceUrl": "https://zenodo.org/records/23721112", "note": "The versioned research package and manuscript are publicly archived on GitHub and Zenodo; availability does not establish correctness or peer review." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "replay_all.py reruns all eight scripts from a clean copy of the frozen archive, compares every record at relative tolerance 1e-9 and checks the headline values, in normal and optimised mode; fourteen negative controls are rejected. GitHub CI repeats both." }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No unaffiliated rerun has been established." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "partial", "note": "Two separate implementations of the four-state checks and standard-library exact fingerprints, and reviewers recomputed load-bearing identities with their own scripts; this is producer-side implementation diversity, not unaffiliated reimplementation." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No proof-assistant formalisation." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "AI-assisted internal review and correctness audits are not external specialist review." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No external editorial peer review." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "passed", "note": "Python 3.11 or later with pinned NumPy, SciPy and SymPy; replay passed locally on macOS and in CI on Ubuntu." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted research", "AI-assisted internal review, two adversarial audits by a different model and a targeted proof audit", "Claude Code: publication packaging and release" ], "humanRole": "Publication authority only; no human research contribution inferred.", "reviewStatus": "Internal AI-assisted review, not external peer review." }, "attributionBoundary": null, "problem": null, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Prepared from the final manuscript (dated 28 October 2026, 16 pages), its verification records and the frozen release archive.", "grandfatheredAtSchemaVersion": null, "keywords": [ "entropy production", "stochastic thermodynamics", "thermodynamic inference", "time irreversibility", "covariance", "Gaussian approximation", "Markov chain", "diffusion", "counterexample" ], "keyResults": [ "Four-state chains with one fixed covariance C(t) = e^{Ft}Σ at every lag, bounded rates, uniform mixing and an injective readout have entropy-production rates ε log((6−κ)/(3−κ)) covering (0, ∞) (Theorem 1, proof with exact checks).", "The Gaussian spectral value of that covariance is exactly 1/3, so it is not a lower bound; at (ε, κ) = (1/4, 1) the true rate is log(5/2)/4 ≈ 0.229 and the overestimate is unbounded in general; the failure persists for bounded readouts, sampled and smoothed records (Section 3 and Section 8, proof).", "Planar diffusions with the Gaussian comparator’s linear drift and state-dependent noise reproduce the same covariance with entropy-production rates filling (0, 1/3]; a Student-type member has rate α/(3(α+1)) (Theorem 2, Proposition 3, proof).", "Reversible gating preserves any centred covariance while multiplying entropy production by ε (Theorem 4, Corollary 5, proof).", "The Raux–Maier–Seifert fourth-order bound recovers 6/(7 log(5/2)) ≈ 93.5% of the exact rate at short lags; a naive kurtosis-discounted bound fails in a random search (Section 6, proof and numerics).", "Open: whether a diffusion with constant noise and nonlinear drift can reproduce the covariance with dissipation below 1/3." ], "reviews": [], "evidencePackage": "Written proofs of every theorem and proposition; exact rational checks of the four-state family in two implementations plus standard-library fingerprints; symbolic Fokker–Planck checks and two-dimensional quadratures for the diffusions; a random-chain kurtosis probe; a replay driver that reruns every script, compares every record and checks the headline values in normal and optimised mode; fourteen semantic negative controls; CI.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "M. 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Saito (2024), Dissipation, quantum coherence, and asymmetry of finite-time cross-correlations.", "url": "https://doi.org/10.1103/PhysRevResearch.6.013273", "doi": "10.1103/PhysRevResearch.6.013273" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:fixed-correlations-weak-dissipation", "attemptIds": [ "ep-attempt:fixed-correlations-weak-dissipation-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "communication" ], "lineageId": null, "accelerationPrimitives": [ "certificate-first", "counterexample-proxy-first", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "counterexample", "description": "Fully observed four-state Markov chains and planar diffusions sharing one fixed time-asymmetric covariance with arbitrarily small entropy production refute the unrestricted Gaussian lower-bound statement of Seara, Machta and Murrell (2021).", "scope": "Exact stationary statistics; fixed covariance with vanishing dissipation needs growing amplitudes or heavy-tailed noise; constant-noise diffusions open." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "The refuted sentence is quoted from the published article; the paper separates the published statement from the phase-randomisation argument in the preprint appendix.", "remainingRisks": [ "The published supplement of Seara et al. was not retrieved.", "Checks rely on Python execution; no proof assistant was used.", "The bounded literature check is not exhaustive priority certification." ] }, "humanJudgmentGates": [ "Publication is authorised; scientific endorsement is not inferred.", "External specialist review and independent reproduction remain open." ], "parentLinks": [], "assuranceTarget": { "dimensions": [ "independentRerun", "specialistReview", "formalVerification", "priorityAssessment" ], "nextAction": "Recheck the four-state identities and the diffusion Fokker–Planck computation in independent software, and ask a specialist whether constant-noise diffusions are known.", "claimCeiling": "Refutation of the unrestricted Gaussian lower-bound statement with proved four-state and diffusion counterexamples; constant-noise diffusions open. 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