{
  "abstract": "A graph-theoretic analysis of the steady-state current noise in master equations under a finite thermodynamic force (affinity) is presented. The incidence matrix twisted by a finite affinity is not orthogonal to the standard cycle space, motivating the introduction of twisted circuit matrices to restore the orthogonality. The resulting twisted-cycle matrix yields an interference-like effect, enabling us to express the signal-to-noise ratio as a quadratic optimization problem in terms of twisted-cycle currents. We apply this framework to a Brownian computation model on a tree-like state-transition diagram with exponential backward branching, finite affinity at each step, and a single reset cycle. In the limit of an infinitely long intended computation path $\\ell$, the Fano factor of the reset current undergoes a transition from noiseless to Poissonian behavior at an affinity equal to the logarithm of the number of immediate predecessors $α$. This corresponds to an easy-hard transition in the computational time complexity [K. Okajima, K. Hukushima, arXiv:2512.24728 ], which is not captured by the thermodynamic uncertainty relation. This transition point precisely characterizes the thermodynamic costs of logically irreversible computation: in the absence of affinity, the reset cost scales as $\\ln \\ell$, whereas reaching the transition point requires a thermodynamic force of order $\\ln α$ per step to counteract backward branching.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. E 114, 044104 (2026)",
  "arxiv": "2605.17838",
  "author_total": 1,
  "authors": [
    {
      "name": "Yasuhiro Utsumi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0m76w168ab8np.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.17838",
  "fulltext_url": null,
  "id": "0m76w168ab8np",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.17838",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.17838",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0m76w168ab8np.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2605.17838",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.17838"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Network analysis for steady-state current fluctuations under finite affinity: Application to Brownian computation",
  "title_text": "Network analysis for steady-state current fluctuations under finite affinity: Application to Brownian computation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/0m76w168ab8np",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/32qy-2v16",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}