{
  "abstract": "We show that a linear damped elastic system can display a Mpemba-like reversal of vibrational relaxation without any nonlinear constitutive response or amplitude-dependent damping. The mechanism is purely modal. For a one-dimensional Kelvin--Voigt elastic medium, the decay rate of the $n$-th vibrational mode scales as $γ_n\\propto n^2$. We formulate relaxation in terms of a positive modal envelope energy, thereby excluding crossings caused merely by oscillation phase. A one-parameter family of initial states is then constructed such that increasing the initial elastic excitation simultaneously reduces the projection onto the slow fundamental mode. In the invariant two-mode subspace, the relaxation-order crossing is obtained analytically and, for this family, occurs at a universal dimensionless time independent of the selected pair of initial states. In the limiting case where the slowest mode is absent, the dominant relaxation rate changes discontinuously, yielding a direct vibrational analogue of the strong Mpemba effect. We further show that the same relaxation-order reversal occurs in the ordinary mechanical vibrational energy, which decreases monotonically despite retaining the oscillatory dynamics of the underlying modes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31268",
  "author_total": 2,
  "authors": [
    {
      "name": "Kiwamu Yoshii"
    },
    {
      "name": "Satoshi Takada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aj50b708hscdv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31268",
  "fulltext_url": null,
  "id": "aj50b708hscdv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31268",
  "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.soft"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7214659333",
  "pdf_url": "https://arxiv.org/pdf/2609.31268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aj50b708hscdv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.31268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31268"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Vibrational Mpemba relaxation in a linear damped elastic system",
  "title_text": "Vibrational Mpemba relaxation in a linear damped elastic system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/aj50b708hscdv",
  "venue": "arXiv",
  "versions": []
}