{
  "abstract": "We consider the full distribution $P_N(A)$ of the dynamical observable $A = - \\sum_{i=1}^N \\ln x_i$ where $x_1, \\dots, x_N$ is a sequence generated by a chaotic map $f(x)$ via $x_{n+1} = f(x_n)$. We study the particular cases where $f(x)$ is the doubling, tent or logistic map, and focus on the limit $N \\gg 1$. Typical fluctuations of $A$ are Gaussian with mean $\\left\\langle A\\right\\rangle$ and variance which are both of order $\\sim N$. We find that the left tail of the distribution ($A < \\left\\langle A\\right\\rangle$) scales as $P_{N}(A) \\sim e^{-NI(A/N)}$, and calculate the rate function $I(a)$ which depends on the map $f(x)$. Interestingly, we find that the right tail of the distribution ($A > \\left\\langle A\\right\\rangle$) follows an anomalous scaling: $P_{N}(A) \\sim e^{-N^{1/3} F((A-\\left\\langle A\\right\\rangle) / N^{2/3})}$. The large-deviation function $F(y)$ has a universal form for the three maps, differing only in the scaling constants. At a critical value $y=y_c$, it exhibits a corner singularity which has the character of a condensation transition. The transition separates between a subcritical phase $0< y<y_c$ in which the fluctuations are Gaussian and arise homogeneously from all of the $x_i$'s, and a supercritical phase $y>y_c$ in which a small fraction of the $x_i$'s give a macroscopic contribution to the fluctuation. Despite this anomalous behavior of the right tail, we find that the cumulants of the distribution $P_N(A)$ grow linearly with $N$ at large $N$, and calculate the associated coefficients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21288",
  "author_total": 2,
  "authors": [
    {
      "name": "Lucianno Defaveri"
    },
    {
      "name": "Naftali R. Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rb34jg02vw0p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21288",
  "fulltext_url": null,
  "id": "1rb34jg02vw0p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21288",
  "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",
      "nlin.CD"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7222529855",
  "pdf_url": "https://arxiv.org/pdf/2610.21288",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rb34jg02vw0p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21288",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21288"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Dynamical phase transition for a logarithm observable in chaotic systems",
  "title_text": "Dynamical phase transition for a logarithm observable in chaotic systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:50Z",
  "url": "https://research.draconitic.com/paper/1rb34jg02vw0p",
  "venue": "arXiv",
  "versions": []
}