{
  "abstract": "Thermodynamic uncertainty relations bound the fluctuations of time-antisymmetric currents. Stochastic efficiency is not one: a ratio of two odd quantities, it is even under path reversal, and for the conventional ratio $-W/Q_h$ no moment exists. We work with the exergetic ratio $η=W/(W+T_0S)$, whose moments exist, and ask how much of its variance a finite perturbation of the dynamics can certify when linear response cannot. The question is specific to nonlinear observables: for every current, and every observable linear in transition counts and residence times, the multiparameter Cramér-Rao bound over rate and site perturbations already equals the variance. For $η$ it does not. The Cramér-Rao bound vanishes on a hyperplane of perturbation directions, while the Barankin multi-point bound, applied to tilted path measures, stays positive there and recovers 75% of the variance of $η$ in a three-state motor model where every linear-response bound is zero. The Gram matrix of tilted Markov-jump path measures is a Feynman-Kac matrix exponential whose potential is the Hellinger integrand of the jump intensities, and the cost of a perturbation is its $χ^2$ divergence, which no dissipation bound controls. The bound captures 1.25-1.57 times the best linear-response bound, and the gain persists on networks of up to sixteen states. For an Ornstein-Uhlenbeck process the construction is exactly solvable: the optimal tilt scales as $T^{-1/2}$ and three test points nearly reach the supremum. Two limits are established. The gain is a short-window effect that disappears as the counts become Gaussian, and the bound cannot be turned into inference: coarse measurements bound $χ^2$ only from below. The construction is a computational instrument for a model in hand, not an uncertainty relation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37940",
  "author_total": 1,
  "authors": [
    {
      "name": "Badr Farih"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c27ac3c6akvdn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37940",
  "fulltext_url": null,
  "id": "c27ac3c6akvdn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37940",
  "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": "W7214917128",
  "pdf_url": "https://arxiv.org/pdf/2609.37940",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c27ac3c6akvdn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2609.37940",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37940"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Blind directions of linear response and the limits of finite-perturbation bounds on efficiency fluctuations",
  "title_text": "Blind directions of linear response and the limits of finite-perturbation bounds on efficiency fluctuations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/c27ac3c6akvdn",
  "venue": "arXiv",
  "versions": []
}