{
  "abstract": "We compare the specific dissipation $Q^{-1}\\left( ω\\right) $ for the Becker, Lomnitz, and Lambert models in linear viscoelasticity. Graphically, the specific dissipation of these models behaves similarly as $ω\\rightarrow 0^{+}$ and $ω\\rightarrow +\\infty$. Furthermore, we obtain analytic formulas for the asymptotic behavior of $Q^{-1}\\left( ω\\right) $ in the Becker and Lomnitz models as $ω\\rightarrow 0^{+}$ and $ω\\rightarrow +\\infty$, where the latter limit coincides with the specific dissipation of the Maxwell model. We also derive a novel closed-form expression for the specific dissipation in the generalized Becker model, $Q_{ν}^{-1}\\left( ω\\right) $, when the parameter $ν\\in \\left( 0,1\\right] $ is rational. When $ν\\rightarrow 0$, we recover the specific dissipation of the Maxwell model, whereas when $ν=1$, we recover that of the original Becker model. In addition, we derive two new closed-form expressions for the specific dissipation for the extended Jeffreys--Lomnitz model $Q_{α}^{-1}\\left( ω\\right) $, the first being valid for $α\\in \\left( 0,1\\right] $, and the second for $α\\in \\left( -\\infty ,1\\right] $. When $α\\rightarrow 0$, we recover the specific dissipation of the Lomnitz model, whereas when $α=1$, we recover that of the Maxwell model. Finally, we conclude that the asymptotic behavior of $Q_{α}^{-1}\\left( ω\\right) $ as $ω\\rightarrow +\\infty $ coincides with the specific dissipation of the Maxwell model. Keywords:",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Mathematics, Vol. 14, No 16 (2026), 2936",
  "arxiv": "2609.05465",
  "author_total": 2,
  "authors": [
    {
      "name": "Juan Luis Gonzalez-Santander"
    },
    {
      "name": "Francesco Mainardi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkda506nhbcwp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05465",
  "fulltext_url": null,
  "id": "dkda506nhbcwp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05465",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.05465",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkda506nhbcwp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.05465",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05465"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Energy dissipation in linear viscoelasticity",
  "title_text": "Energy dissipation in linear viscoelasticity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/dkda506nhbcwp",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.3390/math14162936",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}