{
  "abstract": "The free-energy principle (FEP) and active inference describe adaptive systems through probabilistic generative models and free-energy functionals, whereas integrated information theory (IIT) characterizes intrinsic cause-effect organization. We separate two questions: whether revised IIT quantities admit local free-energy-like representations and whether scalar expected free energy can determine system integrated information. We show that the 2026 IIT intrinsic-differentiation and specification terms admit exact surprisal representations, and hence variational-free-energy representations under exact inference. We then construct noisy binary permutation networks whose causal topology varies while local transition reliability is fixed. In a homogeneous state, all permutations yield the same one-step predictive distribution and state-risk expected free energy under common preferences and observation models, yet revised IIT distinguishes them: multicycle permutations have zero whole-system integration, whereas a single noisy cycle has positive integration at intermediate reliability. For an n-unit noisy single cycle, we derive a closed-form expression for revised system integrated information, prove that the minimum-information partition cuts exactly two causal edges, and show that as n grows the optimal reliability approaches unity, the joint specified-state probability approaches one half, and the maximum integration approaches one ibit. Numerical IIT calculations for n = 2-5 and exhaustive partition enumeration through n = 8 reproduce the analytical results. Thus, local surprisal/free-energy correspondence coexists with global non-equivalence: equal expected free energy does not imply equal revised IIT system integrated information. Any synthesis of IIT with FEP/active inference must retain counterfactual causal information beyond a scalar free-energy value.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03735",
  "author_total": 1,
  "authors": [
    {
      "name": "Katsuaki Tanabe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4p17xwbje1x7m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03735",
  "fulltext_url": null,
  "id": "4p17xwbje1x7m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03735",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "q-bio.NC"
    ],
    [
      "openalex",
      "2805|Embodied and Extended Cognition"
    ]
  ],
  "openalex": "W7220679972",
  "pdf_url": "https://arxiv.org/pdf/2610.03735",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4p17xwbje1x7m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.03735",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03735"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Nonequivalence of expected free energy and revised system integrated information in noisy permutation networks",
  "title_text": "Nonequivalence of expected free energy and revised system integrated information in noisy permutation networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:43Z",
  "url": "https://research.draconitic.com/paper/4p17xwbje1x7m",
  "venue": "arXiv",
  "versions": []
}