{
  "abstract": "Human societies tend to evolve toward increasing scale and complexity, often followed by stagnation and decline. Historical empires provide a prominent example of this trajectory; however, existing quantitative models capture expansion and rarely account for decline within a unified framework. Here, we introduce a minimal dynamical model that describes both growth and collapse in a single formalism. The model yields a closed-form trajectory that generalizes the Gompertz law and admits equivalent maximum-entropy and optimal-control formulations. We show that this functional form captures the rise and fall of fourteen diverse empires across widely varying time scales. Despite substantial historical heterogeneity, all cases follow a common asymmetric rise-peak-decline pattern governed by a small number of interpretable parameters. We identify the mechanism driving this behavior as the chronophage: an exponentially accumulating burden of administrative and coordination costs that offsets the gains of expansion. These findings uncover a general quantitative principle, yielding new insights into how increasing complexity constrains large-scale social systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29202",
  "author_total": 3,
  "authors": [
    {
      "name": "Sabin Roman"
    },
    {
      "name": "Vaishnavi Jayakumar"
    },
    {
      "name": "Karoline Wiesner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5rpe15tdyjvxs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29202",
  "fulltext_url": null,
  "id": "5rpe15tdyjvxs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29202",
  "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",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "3109|Complex Systems and Dynamics"
    ]
  ],
  "openalex": "W7204890673",
  "pdf_url": "https://arxiv.org/pdf/2608.29202",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5rpe15tdyjvxs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.29202",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29202"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A Generalized Gompertz Law for the Rise and Fall of Empires",
  "title_text": "A Generalized Gompertz Law for the Rise and Fall of Empires",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/5rpe15tdyjvxs",
  "venue": "arXiv",
  "versions": []
}