{
  "id": "2402.19157",
  "version": "v3",
  "published": "2024-02-29T13:40:04.000Z",
  "updated": "2024-05-23T11:56:40.000Z",
  "title": "Broken detailed balance and entropy production in directed networks",
  "authors": [
    "Ramón Nartallo-Kaluarachchi",
    "Malbor Asllani",
    "Gustavo Deco",
    "Morten L. Kringelbach",
    "Alain Goriely",
    "Renaud Lambiotte"
  ],
  "comment": "36 pages, 14 figures",
  "categories": [
    "physics.soc-ph",
    "cond-mat.stat-mech",
    "q-bio.NC"
  ],
  "abstract": "The structure of a complex network plays a crucial role in determining its dynamical properties. In this work, we show that the the degree to which a network is directed and hierarchically organised is closely associated with the degree to which its dynamics break detailed balance and produce entropy. We consider a range of dynamical processes and show how different directed network features affect their entropy production rate. We begin with an analytical treatment of a 2-node network followed by numerical simulations of synthetic networks using the preferential attachment and Erd\\\"os-Renyi algorithms. Next, we analyse a collection of 97 empirical networks to determine the effect of complex real-world topologies. Finally, we present a simple method for inferring broken detailed balance and directed network structure from multivariate time-series and apply our method to identify non-equilibrium dynamics and hierarchical organisation in both human neuroimaging and financial time-series. Overall, our results shed light on the consequences of directed network structure on non-equilibrium dynamics and highlight the importance and ubiquity of hierarchical organisation and non-equilibrium dynamics in real-world systems.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2024-05-23T11:56:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "broken detailed balance",
      "non-equilibrium dynamics",
      "directed network structure",
      "entropy production rate",
      "dynamics break detailed balance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}