"detailed balance" meaning in English

{
  "forms": [
    {
      "form": "detailed balances",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "detailed balance (plural detailed balances)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Probability theory",
          "orig": "en:Probability theory",
          "parents": [
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "P_ijπᵢ=P_jiπⱼ,"
        },
        {
          "text": "where P is the Markov transition matrix and πᵢ and πⱼ are the equilibrium probabilities of being in states i and j, respectively."
        }
      ],
      "glosses": [
        "a Markov process is said to show detailed balance if the transition rates between each pair of states i and j in the state space obey"
      ],
      "id": "en-detailed_balance-en-noun-OD3cAs7q",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "probability theory",
          "probability theory"
        ],
        [
          "Markov process",
          "Markov process"
        ]
      ],
      "raw_glosses": [
        "(mathematics, probability theory) a Markov process is said to show detailed balance if the transition rates between each pair of states i and j in the state space obey"
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "a quality of Markov processes",
          "tags": [
            "neuter"
          ],
          "word": "detailliertes Gleichgewicht"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "a quality of Markov processes",
          "word": "detailed balance"
        },
        {
          "code": "he",
          "lang": "Hebrew",
          "roman": "izún meforát",
          "sense": "a quality of Markov processes",
          "tags": [
            "masculine"
          ],
          "word": "איזון מפורט"
        }
      ],
      "wikipedia": [
        "detailed balance"
      ]
    }
  ],
  "word": "detailed balance"
}

{
  "forms": [
    {
      "form": "detailed balances",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "detailed balance (plural detailed balances)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Mathematics",
        "en:Probability theory"
      ],
      "examples": [
        {
          "text": "P_ijπᵢ=P_jiπⱼ,"
        },
        {
          "text": "where P is the Markov transition matrix and πᵢ and πⱼ are the equilibrium probabilities of being in states i and j, respectively."
        }
      ],
      "glosses": [
        "a Markov process is said to show detailed balance if the transition rates between each pair of states i and j in the state space obey"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "probability theory",
          "probability theory"
        ],
        [
          "Markov process",
          "Markov process"
        ]
      ],
      "raw_glosses": [
        "(mathematics, probability theory) a Markov process is said to show detailed balance if the transition rates between each pair of states i and j in the state space obey"
      ],
      "topics": [
        "mathematics",
        "probability-theory",
        "sciences"
      ],
      "wikipedia": [
        "detailed balance"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "a quality of Markov processes",
      "tags": [
        "neuter"
      ],
      "word": "detailliertes Gleichgewicht"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "a quality of Markov processes",
      "word": "detailed balance"
    },
    {
      "code": "he",
      "lang": "Hebrew",
      "roman": "izún meforát",
      "sense": "a quality of Markov processes",
      "tags": [
        "masculine"
      ],
      "word": "איזון מפורט"
    }
  ],
  "word": "detailed balance"
}