{
  "abstract": "Autonomous quantum thermal machines have recently been proposed as physics-based computing substrates where logical inputs and outputs are encoded in temperature gradients. While such ``thermodynamic neurons'' exhibit a clear trade-off between computational fidelity and heat dissipation, the fundamental information-theoretic limits of temperature-encoded computation remain uncharacterized. Here, we derive rigorous bounds linking average error probability, channel capacity, and entropy production for finite-capacity thermal reservoirs operating far from equilibrium. We prove that the minimal dissipation required to achieve a target average error probability $\\langle ξ\\rangle$ diverges as $\\langle ξ\\rangle$ approaches a fundamental minimum error floor $\\epsMin$ imposed by finite-reservoir thermal fluctuations. We further establish a thermodynamic channel capacity that saturates at high dissipation, and quantify the minimal dissipation required for cascaded networks to maintain target fidelity. We demonstrate that the required dissipation grows linearly $\\mathcal{O}(L)$ with network depth for shallow networks, but diverges as the network depth $L$ approaches a fundamental maximum limit $L_{\\max} = \\epsNet/\\epsMin$ imposed by the minimum error floor. Furthermore, under strong noise amplification conditions, the required dissipation can grow up to $\\mathcal{O}(L^3)$. Our framework bridges stochastic thermodynamics, finite-time information theory, and autonomous computation, providing rigorous design principles for energy-efficient analog thermodynamic hardware.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.10027",
  "author_total": 1,
  "authors": [
    {
      "name": "M. W. AlMasri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aya2bpxvz75e4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.10027",
  "fulltext_url": null,
  "id": "aya2bpxvz75e4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.10027",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.10027",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aya2bpxvz75e4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2608.10027",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.10027"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Thermodynamic Cost of Computing with Heat",
  "title_text": "The Thermodynamic Cost of Computing with Heat",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/aya2bpxvz75e4",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/1402-4896/aea665",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}