"phase space" meaning in All languages combined

See phase space on Wiktionary

Noun [English]

Forms: phase spaces [plural]
Etymology: The concept was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré and Josiah Willard Gibbs. Head templates: {{en-noun|~}} phase space (countable and uncountable, plural phase spaces)
  1. (mathematics, physics, dynamical system theory) Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point; Tags: countable, uncountable Categories (topical): Mathematics, Physics, Cybernetics
    Sense id: en-phase_space-en-noun-ZyHovNhP Disambiguation of Cybernetics: 51 49 Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Catalan translations, Terms with Czech translations, Terms with Danish translations, Terms with Dutch translations, Terms with Finnish translations, Terms with French translations, Terms with German translations, Terms with Indonesian translations, Terms with Italian translations, Terms with Japanese translations, Terms with Korean translations, Terms with Mandarin translations, Terms with Polish translations, Terms with Portuguese translations, Terms with Romanian translations, Terms with Russian translations, Terms with Spanish translations, Terms with Swedish translations, Terms with Ukrainian translations Disambiguation of English entries with incorrect language header: 49 51 Disambiguation of Entries with translation boxes: 47 53 Disambiguation of Pages with 1 entry: 50 50 Disambiguation of Pages with entries: 50 50 Disambiguation of Terms with Catalan translations: 50 50 Disambiguation of Terms with Czech translations: 49 51 Disambiguation of Terms with Danish translations: 50 50 Disambiguation of Terms with Dutch translations: 50 50 Disambiguation of Terms with Finnish translations: 49 51 Disambiguation of Terms with French translations: 50 50 Disambiguation of Terms with German translations: 50 50 Disambiguation of Terms with Indonesian translations: 50 50 Disambiguation of Terms with Italian translations: 50 50 Disambiguation of Terms with Japanese translations: 50 50 Disambiguation of Terms with Korean translations: 50 50 Disambiguation of Terms with Mandarin translations: 50 50 Disambiguation of Terms with Polish translations: 50 50 Disambiguation of Terms with Portuguese translations: 50 50 Disambiguation of Terms with Romanian translations: 50 50 Disambiguation of Terms with Russian translations: 50 50 Disambiguation of Terms with Spanish translations: 51 49 Disambiguation of Terms with Swedish translations: 50 50 Disambiguation of Terms with Ukrainian translations: 50 50 Topics: mathematics, natural-sciences, physical-sciences, physics, sciences
  2. (mathematics, physics, dynamical system theory) Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point; Tags: countable, uncountable Categories (topical): Mathematics, Physics, Cybernetics Synonyms: phase-space Hyponyms: phase line, phase plane Derived forms: phase space analysis, phase space trajectory Related terms: configuration space, parameter space, state space, phase diagram, phase integral, phase portrait
    Sense id: en-phase_space-en-noun-ZADF~DEu Disambiguation of Cybernetics: 51 49 Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Catalan translations, Terms with Czech translations, Terms with Danish translations, Terms with Dutch translations, Terms with Finnish translations, Terms with French translations, Terms with German translations, Terms with Indonesian translations, Terms with Italian translations, Terms with Japanese translations, Terms with Korean translations, Terms with Mandarin translations, Terms with Polish translations, Terms with Portuguese translations, Terms with Romanian translations, Terms with Russian translations, Terms with Spanish translations, Terms with Swedish translations, Terms with Ukrainian translations Disambiguation of English entries with incorrect language header: 49 51 Disambiguation of Entries with translation boxes: 47 53 Disambiguation of Pages with 1 entry: 50 50 Disambiguation of Pages with entries: 50 50 Disambiguation of Terms with Catalan translations: 50 50 Disambiguation of Terms with Czech translations: 49 51 Disambiguation of Terms with Danish translations: 50 50 Disambiguation of Terms with Dutch translations: 50 50 Disambiguation of Terms with Finnish translations: 49 51 Disambiguation of Terms with French translations: 50 50 Disambiguation of Terms with German translations: 50 50 Disambiguation of Terms with Indonesian translations: 50 50 Disambiguation of Terms with Italian translations: 50 50 Disambiguation of Terms with Japanese translations: 50 50 Disambiguation of Terms with Korean translations: 50 50 Disambiguation of Terms with Mandarin translations: 50 50 Disambiguation of Terms with Polish translations: 50 50 Disambiguation of Terms with Portuguese translations: 50 50 Disambiguation of Terms with Romanian translations: 50 50 Disambiguation of Terms with Russian translations: 50 50 Disambiguation of Terms with Spanish translations: 51 49 Disambiguation of Terms with Swedish translations: 50 50 Disambiguation of Terms with Ukrainian translations: 50 50 Topics: mathematics, natural-sciences, physical-sciences, physics, sciences
The following are not (yet) sense-disambiguated
Translations (topological space of states of a system): espai de fases [masculine] (Catalan), espai fàsic [masculine] (Catalan), 相空間 /相空间 (xiàngkōngjiān) (Chinese Mandarin), fázový prostor [masculine] (Czech), faserum [neuter] (Danish), faseruimte [feminine] (Dutch), faasiavaruus (Finnish), espace des phases [masculine] (French), Phasenraum [masculine] (German), ruang fase (Indonesian), spazio delle fasi [masculine] (Italian), 位相空間 (isō kūkan) (alt: いそう くうかん) (Japanese), 위상공간 (wisanggonggan) (alt: 位相空間) (Korean), przestrzeń fazowa [feminine] (Polish), espaço de fases [Brazil, masculine] (Portuguese), espaço de fase [Portugal, masculine] (Portuguese), espaço fásico [masculine] (Portuguese), spațiu de fază [neuter] (Romanian), фа́зовое простра́нство (fázovoje prostránstvo) [neuter] (Russian), espacio fásico [masculine] (Spanish), espacio de fases [masculine] (Spanish), fasrum [neuter] (Swedish), фа́зовий про́стір (fázovyj próstir) [masculine] (Ukrainian)
Disambiguation of 'topological space of states of a system': 47 53

Inflected forms

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          "text": "The phase space of a single material point is a manifold M×V*, and the Newton state-space is identifical^([sic]) with M×V.",
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          "text": "2006, Matthew Charles Cargo, Phase Space Approaches to Higher Order WKB Approximations, University of California, Berkeley, page 8,\nTheir energies are those of the level sets p²/2+V(x)=E that enclose an area of 2π hbar (n+1/2) in the classical phase space. Despite embracing a configuration space point of view, these methods have produced a phase space result."
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          "ref": "2007, Helmut Wiedemann, Particle Accelerator Physics, Springer, page 377:",
          "text": "The distribution of particles in phase space is given either by the injector characteristics and injection process or in the case of electron beams by the equilibrium of quantum excitation due to synchrotron radiation and damping.",
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          "word": "phase line"
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          "word": "configuration space"
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          "word": "parameter space"
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          "word": "state space"
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          "word": "phase diagram"
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      "_dis1": "47 53",
      "code": "ca",
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      "sense": "topological space of states of a system",
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      "word": "espai de fases"
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      "word": "espai fàsic"
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      "roman": "xiàngkōngjiān",
      "sense": "topological space of states of a system",
      "word": "相空間 /相空间"
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      "sense": "topological space of states of a system",
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      "sense": "topological space of states of a system",
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      "word": "espace des phases"
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      "sense": "topological space of states of a system",
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      "word": "spazio delle fasi"
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      "alt": "いそう くうかん",
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      "sense": "topological space of states of a system",
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      "alt": "位相空間",
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      "word": "przestrzeń fazowa"
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      "word": "espaço de fases"
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      "word": "espaço de fase"
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      "_dis1": "47 53",
      "code": "pt",
      "lang": "Portuguese",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espaço fásico"
    },
    {
      "_dis1": "47 53",
      "code": "ro",
      "lang": "Romanian",
      "sense": "topological space of states of a system",
      "tags": [
        "neuter"
      ],
      "word": "spațiu de fază"
    },
    {
      "_dis1": "47 53",
      "code": "ru",
      "lang": "Russian",
      "roman": "fázovoje prostránstvo",
      "sense": "topological space of states of a system",
      "tags": [
        "neuter"
      ],
      "word": "фа́зовое простра́нство"
    },
    {
      "_dis1": "47 53",
      "code": "es",
      "lang": "Spanish",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espacio fásico"
    },
    {
      "_dis1": "47 53",
      "code": "es",
      "lang": "Spanish",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espacio de fases"
    },
    {
      "_dis1": "47 53",
      "code": "sv",
      "lang": "Swedish",
      "sense": "topological space of states of a system",
      "tags": [
        "neuter"
      ],
      "word": "fasrum"
    },
    {
      "_dis1": "47 53",
      "code": "uk",
      "lang": "Ukrainian",
      "roman": "fázovyj próstir",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "фа́зовий про́стір"
    }
  ],
  "wikipedia": [
    "Henri Poincaré",
    "Josiah Willard Gibbs",
    "Ludwig Boltzmann",
    "phase space"
  ],
  "word": "phase space"
}
{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "English uncountable nouns",
    "Entries with translation boxes",
    "Pages with 1 entry",
    "Pages with entries",
    "Terms with Catalan translations",
    "Terms with Czech translations",
    "Terms with Danish translations",
    "Terms with Dutch translations",
    "Terms with Finnish translations",
    "Terms with French translations",
    "Terms with German translations",
    "Terms with Indonesian translations",
    "Terms with Italian translations",
    "Terms with Japanese translations",
    "Terms with Korean translations",
    "Terms with Mandarin translations",
    "Terms with Polish translations",
    "Terms with Portuguese translations",
    "Terms with Romanian translations",
    "Terms with Russian translations",
    "Terms with Spanish translations",
    "Terms with Swedish translations",
    "Terms with Ukrainian translations",
    "en:Cybernetics"
  ],
  "derived": [
    {
      "word": "phase space analysis"
    },
    {
      "word": "phase space trajectory"
    }
  ],
  "etymology_text": "The concept was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré and Josiah Willard Gibbs.",
  "forms": [
    {
      "form": "phase spaces",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "phase space (countable and uncountable, plural phase spaces)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "phase line"
    },
    {
      "word": "phase plane"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "configuration space"
    },
    {
      "word": "parameter space"
    },
    {
      "word": "state space"
    },
    {
      "word": "phase diagram"
    },
    {
      "word": "phase integral"
    },
    {
      "word": "phase portrait"
    }
  ],
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "English terms with usage examples",
        "en:Mathematics",
        "en:Physics"
      ],
      "examples": [
        {
          "text": "For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.",
          "type": "example"
        },
        {
          "ref": "1991, Jan J. Slawianowski, Geometry of Phase Spaces, Wiley, page 485:",
          "text": "The phase space of a single material point is a manifold M×V*, and the Newton state-space is identifical^([sic]) with M×V.",
          "type": "quote"
        },
        {
          "text": "2006, Matthew Charles Cargo, Phase Space Approaches to Higher Order WKB Approximations, University of California, Berkeley, page 8,\nTheir energies are those of the level sets p²/2+V(x)=E that enclose an area of 2π hbar (n+1/2) in the classical phase space. Despite embracing a configuration space point of view, these methods have produced a phase space result."
        },
        {
          "ref": "2007, Helmut Wiedemann, Particle Accelerator Physics, Springer, page 377:",
          "text": "The distribution of particles in phase space is given either by the injector characteristics and injection process or in the case of electron beams by the equilibrium of quantum excitation due to synchrotron radiation and damping.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point;"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "physics",
          "physics"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "point",
          "point"
        ],
        [
          "underlying set",
          "underlying set"
        ],
        [
          "state",
          "state"
        ],
        [
          "possible",
          "possible"
        ]
      ],
      "qualifier": "dynamical system theory",
      "raw_glosses": [
        "(mathematics, physics, dynamical system theory) Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point;"
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "physics",
        "sciences"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "English terms with usage examples",
        "en:Mathematics",
        "en:Physics"
      ],
      "glosses": [
        "Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point;\n(less formally) the underlying set of such a topological space.",
        "the underlying set of such a topological space."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "physics",
          "physics"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "point",
          "point"
        ],
        [
          "underlying set",
          "underlying set"
        ],
        [
          "state",
          "state"
        ],
        [
          "possible",
          "possible"
        ]
      ],
      "qualifier": "dynamical system theory; less formally",
      "raw_glosses": [
        "(mathematics, physics, dynamical system theory) Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point;"
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "physics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "phase-space"
    }
  ],
  "translations": [
    {
      "code": "ca",
      "lang": "Catalan",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espai de fases"
    },
    {
      "code": "ca",
      "lang": "Catalan",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espai fàsic"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "xiàngkōngjiān",
      "sense": "topological space of states of a system",
      "word": "相空間 /相空间"
    },
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "fázový prostor"
    },
    {
      "code": "da",
      "lang": "Danish",
      "sense": "topological space of states of a system",
      "tags": [
        "neuter"
      ],
      "word": "faserum"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "topological space of states of a system",
      "tags": [
        "feminine"
      ],
      "word": "faseruimte"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "topological space of states of a system",
      "word": "faasiavaruus"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espace des phases"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "Phasenraum"
    },
    {
      "code": "id",
      "lang": "Indonesian",
      "sense": "topological space of states of a system",
      "word": "ruang fase"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "spazio delle fasi"
    },
    {
      "alt": "いそう くうかん",
      "code": "ja",
      "lang": "Japanese",
      "roman": "isō kūkan",
      "sense": "topological space of states of a system",
      "word": "位相空間"
    },
    {
      "alt": "位相空間",
      "code": "ko",
      "lang": "Korean",
      "roman": "wisanggonggan",
      "sense": "topological space of states of a system",
      "word": "위상공간"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "topological space of states of a system",
      "tags": [
        "feminine"
      ],
      "word": "przestrzeń fazowa"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "topological space of states of a system",
      "tags": [
        "Brazil",
        "masculine"
      ],
      "word": "espaço de fases"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "topological space of states of a system",
      "tags": [
        "Portugal",
        "masculine"
      ],
      "word": "espaço de fase"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espaço fásico"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "topological space of states of a system",
      "tags": [
        "neuter"
      ],
      "word": "spațiu de fază"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "fázovoje prostránstvo",
      "sense": "topological space of states of a system",
      "tags": [
        "neuter"
      ],
      "word": "фа́зовое простра́нство"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espacio fásico"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "espacio de fases"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "topological space of states of a system",
      "tags": [
        "neuter"
      ],
      "word": "fasrum"
    },
    {
      "code": "uk",
      "lang": "Ukrainian",
      "roman": "fázovyj próstir",
      "sense": "topological space of states of a system",
      "tags": [
        "masculine"
      ],
      "word": "фа́зовий про́стір"
    }
  ],
  "wikipedia": [
    "Henri Poincaré",
    "Josiah Willard Gibbs",
    "Ludwig Boltzmann",
    "phase space"
  ],
  "word": "phase space"
}

Download raw JSONL data for phase space meaning in All languages combined (8.2kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-01-18 from the enwiktionary dump dated 2025-01-01 using wiktextract (e4a2c88 and 4230888). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.