{
  "abstract": "Fluctuation--response relations (FRRs) provide a fundamental relation between spontaneous fluctuations and the linear response to external perturbations, yet their validity in non-equilibrium systems remains an open problem. In a general class of noisy, finite-size, mean-field models of coupled phase oscillators, we reveal two types of FRRs in the incoherent phase below the synchronization transition. The first, corresponding to the infinite-size limit (I-FRR), involves the convolution between the external force and the correlation function in the time domain. The second, the finite-size counterpart (F-FRR), is governed by finite-size fluctuations and carries a correction factor: a spectrum function whose roots correspond to eigenvalues, or Landau poles, of the linear operator. The finite-size fluctuations are suppressed in the weak-coupling or strong-noise limits, and F-FRR reduces to I-FRR. Our analytical findings are verified by extensive numerical simulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28834",
  "author_total": 2,
  "authors": [
    {
      "name": "Mrinal Sarkar"
    },
    {
      "name": "Yoshiyuki Y. Yamaguchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5340s8pj1z8b5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28834",
  "fulltext_url": null,
  "id": "5340s8pj1z8b5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28834",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "nlin.AO"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7214323347",
  "pdf_url": "https://arxiv.org/pdf/2609.28834",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5340s8pj1z8b5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.28834",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28834"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Fluctuation--Response Relation in Finite-Size Noisy Coupled Phase Oscillators",
  "title_text": "Fluctuation--Response Relation in Finite-Size Noisy Coupled Phase Oscillators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/5340s8pj1z8b5",
  "venue": "arXiv",
  "versions": []
}