{
  "aliases": null,
  "backlinks": [
    {
      "field": "instance_of",
      "target": "9RVKQJQ5JJ"
    },
    {
      "field": "instance_of",
      "target": "TXC6PZT8CF"
    },
    {
      "field": "instance_of",
      "target": "YBAE5QCH1A"
    },
    {
      "field": "defines",
      "target": "XHXQDYAW3M"
    }
  ],
  "body": "\n## Summary\n\nAn interacting particle system is a continuous-time Markov process on configurations of a lattice or graph, in which each site carries a state.\nThe state at a site changes at rates that depend on the states of nearby sites.\nEach local change is simple, but infinitely many sites interact, and the system can show phase transitions.\nMain examples are the [[contact process|9RVKQJQ5JJ]], the [[voter model|YBAE5QCH1A]], the [[exclusion process|TXC6PZT8CF]] and stochastic dynamics of the [[Ising model|R0KGM32QN6]].\nThey model epidemics, opinions, traffic and magnets.\n\n## Explanations\n\n### L1 human\n\nPut a person at each point of an infinite grid, each healthy or sick.\nA sick person recovers after a random time, and a healthy person gets sick at a rate that grows with the number of sick neighbours.\nEach person follows simple local rules, yet the whole grid may behave in very different ways: the illness may die out or spread forever.\nInteracting particle systems are the models of this kind.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "60K35",
      "82C22"
    ],
    "name": "Interacting particle system",
    "same_as": {
      "wikidata": "Q6045167",
      "wikipedia": "Interacting particle system"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Interacting_particle_system"
      }
    ],
    "specializes": [
      "4HS3C12472"
    ],
    "tag": "GR49AM3PSZ"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/GR49AM3PSZ/",
  "links": [
    {
      "field": "specializes",
      "target": "4HS3C12472"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/GR49AM3PSZ.md",
  "msc": [
    "60K35",
    "82C22"
  ],
  "name": "Interacting particle system",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/GR4/GR49AM3PSZ.md",
  "status": null,
  "tag": "GR49AM3PSZ",
  "uri": "m2://GR49AM3PSZ",
  "url": "https://math2.tamnd.com/wiki/interacting-particle-system/",
  "writing": {
    "tag": "GR49AM3PSZ",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}