{
  "abstract": "Thermodynamic uncertainty relations connect current fluctuations to dissipation and, in certain settings, can emerge from underlying fluctuation-response relations. However, in underdamped dynamics, conventional mean-current uncertainty relations can fail, and the underlying connection between fluctuations, response, and dissipation remains elusive. Here, we uncover this connection by deriving an exact finite-time fluctuation-response equality for underdamped Langevin dynamics, which is valid for arbitrary time-dependent driving and general additive observables. The equality yields sharp response bounds and a variational characterization of the dynamically generated variance. Choosing the perturbation along the irreversible probability flow, we obtain an experimentally accessible friction-response thermodynamic uncertainty relation that is saturable at any finite observation time. It provides both an exact variational principle for entropy production and a weak-noise coherence-dissipation bound for underdamped limit cycles. We further show that the conventional uncertainty factor of velocity-resolved currents can decay exponentially with dissipation, even in driven free diffusion, whereas the friction-response factor retains its universal lower bound. These results establish response, rather than the mean current itself, as the quantity directly linking fluctuations and dissipation in underdamped dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.20013",
  "author_total": 4,
  "authors": [
    {
      "name": "Tan Van Vu"
    },
    {
      "name": "Van Tuan Vo"
    },
    {
      "name": "Ruicheng Bao"
    },
    {
      "name": "Keiji Saito"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hqpzvpsmr4zm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.20013",
  "fulltext_url": null,
  "id": "6hqpzvpsmr4zm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.20013",
  "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"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7203865992",
  "pdf_url": "https://arxiv.org/pdf/2608.20013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hqpzvpsmr4zm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2608.20013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.20013"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Exact Fluctuation-Response Relations for Underdamped Langevin Dynamics",
  "title_text": "Exact Fluctuation-Response Relations for Underdamped Langevin Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/6hqpzvpsmr4zm",
  "venue": "arXiv",
  "versions": []
}