{
  "id": "1708.04004",
  "version": "v1",
  "published": "2017-08-14T04:24:01.000Z",
  "updated": "2017-08-14T04:24:01.000Z",
  "title": "Entropy production and flux during collective motion near criticality",
  "authors": [
    "Emanuele Crosato",
    "Ramil Nigmatullin",
    "Joseph T. Lizier",
    "Mikhail Prokopenko"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We study self-organisation of collective motion as a thermodynamic phenomenon, in the context of the second law of thermodynamics. It is expected that the coherent/ordered motion can only self-organise in the presence of entropy flux from the system of moving particles to the environment. We aim to explicitly quantify the entropy flux from a system of simulated self-propelled particles to its environment, as well as the total entropy production of the whole system, and contrast it with the changes in the system's configuration entropy. In doing so, we adapt a thermodynamic formulation of the (sensitivity of) entropy flux in terms of Fisher information and the curvature of the configuration entropy, which has also been derived in this study statistically mechanically. This allows us to systematically investigate the behaviour of the system by varying two control parameters that drive a kinetic phase transition. Our results identify critical regimes and show that during the phase transition, where the configuration entropy of the system decreases, the entropy flux intensifies, while its sensitivity diverges. The total entropy production is shown to be alway positive, thus preserving the second law. Importantly, the ratio of the rate of change of the configuration entropy to the entropy flux is shown to be maximal at the criticality, suggesting that self-organisation exhibits its highest efficiency at criticality. We also provide interpretations of these results in terms of both computational and thermodynamic balances, arguing that both balances are stressed during the phase transition. Additionally, this study provides an information geometric interpretation of the sensitivity of the entropy flux as the difference between two curvatures: the curvature of the free entropy, captured by the Fisher information, and the curvature of the configuration entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-14T04:24:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "collective motion",
      "total entropy production",
      "criticality",
      "thermodynamic",
      "second law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}