phase space
nounEtymology The concept was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré and Josiah Willard Gibbs.
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Mathematics, Natural sciences, Physical sciences, Physics, Sciences 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;
Dynamical system theory
- For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.
- 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:
2 more examples
- 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:
› Given a (dynamical) system, any topological…
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Mathematics, Natural sciences, Physical sciences, Physics, Sciences the underlying set of such a topological space.
Dynamical system theory; less formally
- Derived terms
- phase space analysis, phase space trajectory
- Related terms
- configuration space, parameter space, phase diagram, phase integral, phase portrait, state space
- Hyponyms
- phase line, phase plane