{
  "handle": "ShannonEntropy",
  "ref": "ShannonEntropy#a177",
  "stub": "a177",
  "semaId": "sema:ShannonEntropy#mh:SHA-256:a1774e05a3085b62748089790da6da7581e12e1144cab18adf622cb9059b1142",
  "layer": "Infrastructure",
  "category": "Primitives",
  "gloss": "The average surprise of a distribution: how many bits it takes to predict an outcome",
  "mechanism": "For a discrete distribution P = {p_i} over states i, H(P) = -sum_i p_i log p_i, the expected self-information -log p_i of an outcome. Rare outcomes carry much information, likely ones little. H is maximal (log m for m states) when all states are equally likely and zero when all probability sits on one state. Applied to a system's possible configurations, high H means many weakly constrained configurations (variability, flexibility, exploration) and low H means strong constraints (regularity, coordination). Use log base 2 to measure in bits.",
  "invariants": [
    "H is non-negative and zero only for a distribution concentrated on one state",
    "H is maximal for the uniform distribution over the state space",
    "H depends only on the probabilities, not on what the states are or how they are ordered"
  ],
  "failureModes": [
    "State-space dependence: the same system yields different entropies under different state definitions or binnings, so values are comparable only within one state space",
    "Finite-sample bias: entropy estimated from few samples is biased low",
    "Reading low entropy as 'good order' without asking what constrains it"
  ],
  "ring": 0,
  "tier": 0,
  "aliases": {},
  "buildsOn": [],
  "usedBy": [
    {
      "handle": "DegreeEntropy",
      "type": "references",
      "alias": "shannon_entropy",
      "url": "/knowledge-graph/DegreeEntropy/",
      "json": "/knowledge-graph/DegreeEntropy.json"
    },
    {
      "handle": "SpectralEntropy",
      "type": "references",
      "alias": "shannon_entropy",
      "url": "/knowledge-graph/SpectralEntropy/",
      "json": "/knowledge-graph/SpectralEntropy.json"
    },
    {
      "handle": "JensenShannonDivergence",
      "type": "references",
      "alias": "shannon_entropy",
      "url": "/knowledge-graph/JensenShannonDivergence/",
      "json": "/knowledge-graph/JensenShannonDivergence.json"
    }
  ],
  "sources": {
    "research": [],
    "works": [
      {
        "kind": "thesis",
        "label": "Kevin Do, PhD thesis on ant collective behaviour (NCSU, 2026)",
        "note": "Ch. 1.3.1, Eqs. 1.3-1.5",
        "url": ""
      }
    ],
    "homePage": false
  },
  "url": "/knowledge-graph/ShannonEntropy/",
  "graphUrl": "/knowledge-graph#ShannonEntropy",
  "directory": "/knowledge-graph/patterns.json"
}