{
  "abstract": "We consider a measured system $X$ containing a parameter $θ$ of interest and the problem of estimating this parameter by observing a second, coupled measurement system $Y$. We show that, in thermodynamic equilibrium, the Fisher information of $Y$ associated with the parameter is bounded by that of $X$, implying that conservative interactions between $X$ and $Y$ reduce the precision of parameter estimation. Conversely, out of equilibrium, we show that the Fisher information of $Y$ can exceed that of $X$, so that non-conservative interactions can potentially increase the precision of parameter estimation. For idealized, back-action-free measurements, where the coupling to $Y$ does not perturb $X$, we derive a speed limit for the increase of Fisher information of $Y$. This speed limit only depends on the properties of the measured system $X$ and places a fundamental bound on the precision of any back-action-free measurement. As a corollary, we obtain a generalized Cramér-Rao bound (CRB) for time-averaged estimators. We illustrate our results for linear dynamics and suggest a scheme for disturbance-free non-equilibrium sensing with improved accuracy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32252",
  "author_total": 2,
  "authors": [
    {
      "name": "Hiroyuki Odajima"
    },
    {
      "name": "Andreas Dechant"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01fpvpc77w2m1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32252",
  "fulltext_url": null,
  "id": "01fpvpc77w2m1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32252",
  "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.stat-mech"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7223664097",
  "pdf_url": "https://arxiv.org/pdf/2610.32252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01fpvpc77w2m1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.32252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32252"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Measurement speed limit and Cramér-Rao bound for time-averaged estimators",
  "title_text": "Measurement speed limit and Cramér-Rao bound for time-averaged estimators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:15Z",
  "url": "https://research.draconitic.com/paper/01fpvpc77w2m1",
  "venue": "arXiv",
  "versions": []
}