{
  "abstract": "In the paper J. Phys. A: Math. Theor. 53 (2020), 345303, the limiting mutual information between two intervals separated by one lattice site in a free-fermion chain was evaluated. The calculation replaces the entropy function by a regularized version depending on $\\varepsilon>0$, takes the block lengths to infinity, and only then lets $\\varepsilon$ tend to zero. We prove that the opposite order gives the same constant $2\\log2-1$. Moreover, we show that the same limit is obtained whenever both block lengths tend to infinity and $\\varepsilon$ tends to zero simultaneously, with no restriction on their relative rates. In fact, the error caused by the regularization is bounded by $(1+\\varepsilon)\\log(1+\\varepsilon)-\\varepsilon\\log\\varepsilon$, uniformly in both block lengths.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08210",
  "author_total": 2,
  "authors": [
    {
      "name": "Carlo Bellavita"
    },
    {
      "name": "Jani A. Virtanen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2y62krx1x2qk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08210",
  "fulltext_url": null,
  "id": "d2y62krx1x2qk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08210",
  "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",
      "math.FA"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7212065862",
  "pdf_url": "https://arxiv.org/pdf/2609.08210",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2y62krx1x2qk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08210",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08210"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Interchanging limits in the mutual information of two intervals separated by one site",
  "title_text": "Interchanging limits in the mutual information of two intervals separated by one site",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/d2y62krx1x2qk",
  "venue": "arXiv",
  "versions": []
}