{
  "abstract": "Eliminating stiff internal coordinates can preserve equilibrium while changing kinetics, and a finite-time coarse-graining error does not by itself control a zero-frequency transport observable. We study a reversible overdamped Langevin model with constant microscopic mobility and nonlinear soft constraints, Uϵ(x, y; γ) = V (x− Fγ) + |y − g(x)|2 2ϵ , where V may be nonquadratic and nonconvex. An exact coordinate transformation factorizes the equilibrium measure but produces a nontrivial kinetic metric. For any mean-zero source depending only on x, we prove a direct zero-frequency comparison between the full microscopic inverse response Rϵ and the constrained geometric response R0: 0 ≤ R0 −Rϵ ≤ ϵmT 2 Eπ∥Dw0∥2F , where w0 is the source-specific corrector derived from the effective Poisson equation. The bound contains no inverse global spectral gap. For a one-dimensional translated potential, the conjugateforce friction closes explicitly and admits a certified first finite-stiffness correction with two-sided O(ϵ2) remainder bounds. We then derive a mechanism test: any autonomous hidden-history model for which two-time forces are conditionally standard Gaussian with history-dependent correlation must have a nonnegative connected fourth quantity K4(t). A fully reversible nonlinear constant-mobility Langevin model violates this condition: K4,ϵ(t) < 0 for a nonzero short-time interval at every finite ϵ, while its constrained limit satisfies K4(t) < 0 for every t > 0. The all-time sign is certified by a five-dimensional outward-rounded interval Schur test controlling the infinite even sector of the generator. Integer interval arithmetic, independent primal–dual calculations of the full two-dimensional process, and a reversible finite-volume discretization provide mutually distinct checks. These results are a controlled response and model-discrimination theory for a specified soft-constrained class; they do not constitute a general theory of glass formation or a bulk shear-viscosity prediction.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, University of Maryland, 4176 Campus Drive, College Park, MD, USA, 20742-4015"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Yueer Yang",
      "orcid": "0009-0003-7161-4499"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ep60snfm0mq5m.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15009185/v1",
  "fulltext_url": null,
  "id": "ep60snfm0mq5m",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009185/v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213957781",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15009185/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/ep60snfm0mq5m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "10.26434/chemrxiv.15009185",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009185/v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Certified Zero-Frequency Response and a Fourth-Order Mechanism Test for Nonlinear Soft-Constrained Langevin Dynamics",
  "title_text": "Certified Zero-Frequency Response and a Fourth-Order Mechanism Test for Nonlinear Soft-Constrained Langevin Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:21Z",
  "url": "https://research.draconitic.com/paper/ep60snfm0mq5m",
  "venue": "ChemRxiv",
  "versions": []
}