Phase space

In mathematics and physics, a phase space of a dynamical system is a mathematical space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space.

Description

For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.

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

See also

General

• Phase line, 1-dimensional case
• Phase plane, 2-dimensional case
• Phase portrait
• Phase space method
• Parameter space
• Separatrix

Applications

• Optical phase space
• State space (controls) for information about state space (similar to phase state) in control engineering.
• State space for information about state space with discrete states in computer science.
• Molecular dynamics

Mathematics

• Cotangent bundle
• Dynamic system
• Symplectic manifold
• Wigner-Weyl transform

Physics

• Classical mechanics
• Hamiltonian mechanics
• Lagrangian mechanics
• State space (physics) for information about state space in physics
• Phase space formulation of quantum mechanics

External links

• Phase space @ Wikipedia.org