{
  "abstract": "The Landauer principle is usually understood as a cost of computation: erasing information demands a minimum dissipation of heat. Here we ask whether this cost can itself carry information. We show that the minimal heat dissipated by a circuit that multiplies two integers and erases its inputs is set by the factorization structure of the product: products involving few primes are minimally irreversible and thus dissipate little heat, while highly composite products must dissipate more. Measuring the heat of a multiplier working at the Landauer limit would thus amount to a number-theoretic test. However, we argue that this signature is inaccessible in practice: a device approaching the Landauer limit would require computing all factorizations during its design, while a modular circuit with reusable components would not approach the Landauer bound. As an illustration, we estimate the heat generated by a multiplier in a positional base, showing that it destroys the factorization-specific signature and dissipates far more heat. The thermodynamic cost of multiplication therefore depends on factorization, but this dependence cannot be exploited by modular computing architectures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Vilimelis Pau"
    },
    {
      "name": "Dominic Dall'Osto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ttgxfzgxqff4.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "7ttgxfzgxqff4",
  "issns": [],
  "landing_url": "https://hal.science/hal-05743009v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
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      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.math.math-nt"
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      "1.phys.cond"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05743009/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ttgxfzgxqff4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:31Z",
      "native_id": "hal-05743009",
      "source": "hal",
      "url": "https://hal.science/hal-05743009v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-nt",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.cond",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "hal:2.phys.cond.cm-sm",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A factorization-dependent Landauer bound for multiplication, and why it cannot be exploited",
  "title_text": "A factorization-dependent Landauer bound for multiplication, and why it cannot be exploited",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:31Z",
  "url": "https://research.draconitic.com/paper/7ttgxfzgxqff4",
  "venue": "HAL",
  "versions": []
}