Dictionary

phase space en · NOUN

Etymology

The concept was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré and Josiah Willard Gibbs.

Meanings

1. (countable, qualifier:dynamical system theory, uncountable) 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;
   • The phase space of a single material point is a manifold M×V*, and the Newton state-space is identifical^([sic]) with M×V. 1991, Jan J. Slawianowski, Geometry of Phase Spaces, Wiley, page 485:
   • 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.
   • 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. 2007, Helmut Wiedemann, Particle Accelerator Physics, Springer, page 377:
2. (countable, qualifier:dynamical system theory; less formally, uncountable) 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.

Forms

Deriveds

phase space analysis · phase space trajectory

Hyponyms

phase line · phase plane

Relateds

phase portrait · parameter space · phase integral · state space · phase diagram · configuration space

Translations (23)

pt espaço fásico (topological space of states of a system) · es espacio de fases (topological space of states of a system) · pt espaço de fase (topological space of states of a system) · de Phasenraum (topological space of states of a system) · fr espace des phases (topological space of states of a system) · ko 위상공간 (topological space of states of a system) · nl faseruimte (topological space of states of a system) · fi faasiavaruus (topological space of states of a system) · pt espaço de fases (topological space of states of a system) · pl przestrzeń fazowa (topological space of states of a system) · it spazio delle fasi (topological space of states of a system) · da faserum (topological space of states of a system) · ca espai fàsic (topological space of states of a system) · ru фа́зовое простра́нство (topological space of states of a system) · id ruang fase (topological space of states of a system) · uk фа́зовий про́стір (topological space of states of a system) · ca espai de fases (topological space of states of a system) · cmn 相空間 /相空间 (topological space of states of a system) · es espacio fásico (topological space of states of a system) · ro spațiu de fază (topological space of states of a system) · sv fasrum (topological space of states of a system) · cs fázový prostor (topological space of states of a system) · ja 位相空間 (topological space of states of a system)

wikipedia: Josiah Willard Gibbs · wikipedia: Henri Poincaré · wikipedia: Ludwig Boltzmann