{
  "abstract": "A driven colloidal rotor sustains a circulating current whose fluctuations one would like to bound. Any such bound rests on how strongly the current responds to a perturbation and on how much extra dissipation that perturbation costs, so there is a well-posed question of where to push: the response per unit Onsager-Machlup cost depends on the radius at which the probe acts, and is maximised at a definite one. We answer this for the Brownian gyrator and a quadrupolar shear under a Gaussian envelope, a probe chosen so that linear response is exactly blind to it at every observation window, so that the entire signal is second order. The problem separates: the cost is radial and does not see the circulation, while the response lives in the $m=3$ angular sector, where the resolvent reduces to Kummer's equation with $b=4$ and the susceptibility is a hypergeometric function of the envelope width. Maximising the ratio gives the optimal probing radius in closed form. It is set by whichever of the system's two clocks is faster: for weak driving $r^*=1.1264\\sqrt{D/γ}$, the thermal radius of the trap, and for strong driving $r^*=1.5563\\sqrt{D/Ω}$, the distance diffused in one radian of rotation, with the trap stiffness dropping out entirely. The crossover is at $Ω=γ$. Both limits, and the prefactors, are confirmed against direct simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24748",
  "author_total": 1,
  "authors": [
    {
      "name": "Badr Farih"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/chb81tyf1szwj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24748",
  "fulltext_url": null,
  "id": "chb81tyf1szwj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24748",
  "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"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7214005380",
  "pdf_url": "https://arxiv.org/pdf/2609.24748",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/chb81tyf1szwj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24748",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24748"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Optimal probing scale for current fluctuations in a Brownian gyrator",
  "title_text": "Optimal probing scale for current fluctuations in a Brownian gyrator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/chb81tyf1szwj",
  "venue": "arXiv",
  "versions": []
}