{
  "abstract": "Einstein relations connect carrier mobility to macroscopic transport coefficients and constitute a fundamental link between microscopic dynamics and transport. In phonon hydrodynamics, this connection is conventionally local: the drift-induced thermal conductivity is proportional to the local drift mobility. Here we show that this relation becomes intrinsically nonlocal under spatial confinement. We derive a nonlocal Einstein relation, $κ_H(y) = \\int P(y-y')μ(y'),dy'$, in which hydrodynamic thermal conductivity $κ_H(y)$ at one position depends on collective drift mobility $μ(y')$ across the entire cross-section of the channel. In the small-Knudsen-number limit, our nonlocal theory recovers the viscous heat equation and the local Einstein relation. At finite Knudsen number, nonlocality produces intrinsic boundary slip and distinct size-scaling behavior of the drift mobility $μ$ and hydrodynamic thermal conductivity $κ_H(y)$. First-principles calculations for graphite show that nonlocality broadens the channel-size window over which thermal conductivity exhibits superlinear size dependence. Temperature-dependent simulations further show that the nonlocal theory captures the emergence of a hydrodynamic peak in thermal conductivity normalized by ballistic conductance, whereas the local theory fails to accurately predict its magnitude. Our results establish a microscopic connection between collective phonon mobility and heat conduction beyond local hydrodynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35109",
  "author_total": 3,
  "authors": [
    {
      "name": "Guanda Quan"
    },
    {
      "name": "Ronggui Yang"
    },
    {
      "name": "Xin Qian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fjzhbdcfc1s8s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35109",
  "fulltext_url": null,
  "id": "fjzhbdcfc1s8s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35109",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "openalex",
      "2505|Thermal properties of materials"
    ]
  ],
  "openalex": "W7223781848",
  "pdf_url": "https://arxiv.org/pdf/2610.35109",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fjzhbdcfc1s8s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.35109",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35109"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Nonlocal Einstein Relation in Confined Phonon Hydrodynamics",
  "title_text": "Nonlocal Einstein Relation in Confined Phonon Hydrodynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/fjzhbdcfc1s8s",
  "venue": "arXiv",
  "versions": []
}