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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;
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Qualifier: dynamical system theory
Topics: mathematics, natural-sciences, physical-sciences, physics, sciences
Examples
- For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.
- 2006, Matthew Charles Cargo, Phase Space Approaches to Higher Order WKB Approximations, University of California, Berkeley, page 8, Their 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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; (less formally) the underlying set of such a topological space.
the underlying set of such a topological space.
Definition source: English Wiktionary via Wiktextract
Usage: countable, uncountable
Qualifier: dynamical system theory; less formally
Topics: mathematics, natural-sciences, physical-sciences, physics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
(physics) an ideal space in which the coordinate dimensions represent the variables that are required to describe a system or substance
Definition source: Princeton WordNet 3.0
Examples
- a multidimensional phase space
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Broader terms: space, infinite
Narrower terms: dynamical system
The concept was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré and Josiah Willard Gibbs.
Across languages
Translations
23 source translations are retained for this English entry.
-
Catalan:
espai de fases
— topological space of states of a system
-
Catalan:
espai fàsic
— topological space of states of a system
-
Chinese Mandarin:
相空間 /相空间
(xiàngkōngjiān)
— topological space of states of a system
-
Czech:
fázový prostor
— topological space of states of a system
-
Danish:
faserum
— topological space of states of a system
-
Dutch:
faseruimte
— topological space of states of a system
-
Finnish:
faasiavaruus
— topological space of states of a system
-
French:
espace des phases
— topological space of states of a system
-
German:
Phasenraum
— topological space of states of a system
-
Indonesian:
ruang fase
— topological space of states of a system
-
Italian:
spazio delle fasi
— topological space of states of a system
-
Japanese:
位相空間
(isō kūkan)
— topological space of states of a system
-
Korean:
위상공간
(wisanggonggan)
— topological space of states of a system
-
Polish:
przestrzeń fazowa
— topological space of states of a system
-
Portuguese:
espaço de fases
— topological space of states of a system
-
Portuguese:
espaço de fase
— topological space of states of a system
-
Portuguese:
espaço fásico
— topological space of states of a system
-
Romanian:
spațiu de fază
— topological space of states of a system
-
Russian:
фа́зовое простра́нство
(fázovoje prostránstvo)
— topological space of states of a system
-
Spanish:
espacio fásico
— topological space of states of a system
-
Spanish:
espacio de fases
— topological space of states of a system
-
Swedish:
fasrum
— topological space of states of a system
-
Ukrainian:
фа́зовий про́стір
(fázovyj próstir)
— topological space of states of a system
