{
  "abstract": "We derive a sharp upper bound on the quasi-steady temperature rise of a sensor of arbitrary shape and known thermometric volume $V_\\mathrm{s}$, placed anywhere inside a region enclosed by an isothermal reference surface. The bound also requires the total heat power generated in the region $\\dot{Q}_\\mathrm{r}$ and a lower bound on its thermal conductivity $κ_{\\scriptscriptstyle{\\mathcal {V}_{\\mathrm{r}}}}$. It is otherwise independent of the heat-source distribution, domain shape, and source--sensor distance. For $\\dot Q_\\mathrm{r}=50~\\mathrm{pW}$, $κ_{\\scriptscriptstyle{\\mathcal{V}_{\\mathrm r}}} =0.1~\\mathrm{W\\,m^{-1}K^{-1}}$, and $V_{\\mathrm s}$ equal to the volume of a $60~\\mathrm{nm}$-diameter sphere, the theorem permits a maximum temperature rise of approximately $2~\\mathrm{mK}$. Neither source localization nor uncertain source--sensor separation can therefore account for reported kelvin-scale intracellular readings under steady-state heat conduction. The result applies to sensors based on nanodiamonds, upconversion nanoparticles, fluorescent polymer beads, and core--shell quantum dots.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24340",
  "author_total": 1,
  "authors": [
    {
      "name": "Taras Plakhotnik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bq2c1twf3w9am.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24340",
  "fulltext_url": null,
  "id": "bq2c1twf3w9am",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24340",
  "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",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.class-ph"
    ],
    [
      "openalex",
      "2505|Thermal properties of materials"
    ]
  ],
  "openalex": "W7223004802",
  "pdf_url": "https://arxiv.org/pdf/2610.24340",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bq2c1twf3w9am.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2610.24340",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24340"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Maximum-Temperature Theorem for a Nanothermometer",
  "title_text": "Maximum-Temperature Theorem for a Nanothermometer",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:16Z",
  "url": "https://research.draconitic.com/paper/bq2c1twf3w9am",
  "venue": "arXiv",
  "versions": []
}