{
  "abstract": "Characterizing dynamical organization in time series requires distinguishing the diversity of accessible states from uncertainty in their temporal transitions. Here we introduce a state-transition information space based on two normalized entropy measures derived from ordinal patterns: K_q, quantifying ordinal-state diversity, and K_t, quantifying transition uncertainty. Their joint K_t-K_q representation provides a two-dimensional framework in which dynamical regimes and their temporal evolution can be examined. Theoretical properties establish the bounded relation 0 <= K_t <= K_q <= 1, while canonical time series identify distinct empirical domains ranging from ordered dynamics to near-maximal randomness. Sliding-window analysis further shows that systems can exhibit temporal trajectories through the K_t-K_q plane rather than remaining at a fixed dynamical state. Application to 1,879 monthly naturalized streamflow records from the U.S. rivers shows that river dynamics occupy a distinct intermediate region between ordered and highly disordered regimes. Moreover, river positions shift systematically toward higher K_t and K_q with increasing drainage area, revealing scale-dependent organization of streamflow dynamics. The framework therefore provides a compact means of comparing state diversity, transition uncertainty, and their temporal and spatial organization across time-series systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38191",
  "author_total": 3,
  "authors": [
    {
      "name": "Dragutin T Mihailović"
    },
    {
      "name": "Vijay P. Singh"
    },
    {
      "name": "Slavica Malinović-Milićević"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04wqbgbmrnmps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38191",
  "fulltext_url": null,
  "id": "04wqbgbmrnmps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38191",
  "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",
      "physics.data-an"
    ],
    [
      "openalex",
      "2002|Complex Systems and Time Series Analysis"
    ]
  ],
  "openalex": "W7215126490",
  "pdf_url": "https://arxiv.org/pdf/2609.38191",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04wqbgbmrnmps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.38191",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38191"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    }
  ],
  "title": "A State-Transition Information Space for Time-Series Dynamics: Theory and Application",
  "title_text": "A State-Transition Information Space for Time-Series Dynamics: Theory and Application",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/04wqbgbmrnmps",
  "venue": "arXiv",
  "versions": []
}