{
  "abstract": "We investigate a discontinuous route from integrability to chaos using a confined stochastic random walk and a deterministic stadium-like billiard. In both systems, the stationary diffusive observable exhibits a finite jump at the transition: it vanishes at the unperturbed limit but approaches a finite, geometry-controlled value for arbitrarily small nonzero perturbations, providing the characteristic order-parameter signature of a first-order transition. Despite this discontinuity, the relaxation timescale diverges as the transition is approached, revealing critical slowing down. Both models exhibit normal diffusion with $β=1/2$, a perturbation-independent stationary state with $α=0$, and a crossover iteration scaling as $n_x\\proptoλ^{-2}$, yielding $z=-2$, where $λ$ denotes the corresponding perturbation parameter. The common exponent set $(α,β,z)=(0,1/2,-2)$ originates from the same coarse-grained mechanism: normal diffusion within a finite accessible domain with a diffusion coefficient that vanishes quadratically at the transition. The agreement between stochastic transport and deterministic chaotic scattering provides strong evidence for a common class of discontinuous dynamical transitions and extends the statistical-mechanics description of phase transitions to integrability-breaking dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13616",
  "author_total": 4,
  "authors": [
    {
      "name": "Anne Ketri P. da Fonseca"
    },
    {
      "name": "Marcelo de Almeida Presotto"
    },
    {
      "name": "Diego F. M. Oliveira"
    },
    {
      "name": "Edson D. Leonel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ayy8dpcrz22hx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13616",
  "fulltext_url": null,
  "id": "ayy8dpcrz22hx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13616",
  "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",
      "nlin.CD"
    ],
    [
      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
  ],
  "openalex": "W7213275746",
  "pdf_url": "https://arxiv.org/pdf/2609.13616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ayy8dpcrz22hx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.13616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13616"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "First-order integrability-breaking phase transitions in dynamical systems",
  "title_text": "First-order integrability-breaking phase transitions in dynamical systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/ayy8dpcrz22hx",
  "venue": "arXiv",
  "versions": []
}