phase space
Noun: 1. A conceptual mathematical space: In physics and mathematics, phase space is an abstract space in which all possible states of a dynamical system are represented. Each point in this space corresponds to a unique state of the system, defined by the values of all its position and momentum variables (or other conjugate variables).
The term "phase space" is used to describe and analyze the complete state and evolution of a system in classical mechanics, statistical mechanics, and other fields of physics and applied mathematics. - The behavior of the pendulum can be fully described by a trajectory in its phase space. - In statistical mechanics, the ensemble of all possible microstates of a system is represented as a set of points in phase space.
- "to traverse phase space": Refers to a system's evolution, where its representative point moves along a path (trajectory) in phase space.
- As the chaotic system evolves, its point in phase space traverses a complex, non-repeating path.
- "volume of phase space": A measure related to the number of possible microstates of a system, central to statistical mechanics.
- The entropy of the system is related to the logarithm of the volume of phase space it occupies.
- Phase portrait (n): A geometric representation of the trajectories of a dynamical system in the phase plane (a 2D phase space).
- The phase portrait revealed the stability of the equilibrium points.
- State space (n): A more general term, often synonymous with phase space in many contexts, but can also refer to spaces using different variables (e.g., not necessarily conjugate momenta).
- The system's dynamics were modeled in a six-dimensional state space.
- State space: The abstract space encompassing all possible states of a system.
Given the technical nature of the term, standard phrasal verbs and idioms are not applicable. Key related concepts include: - Trajectory: The path traced by the system's representative point in phase space over time. - Dimension: The number of coordinates (variables) needed to define phase space (e.g., for N particles in 3D, it is 6N-dimensional). - Hamiltonian dynamics: A formalism where the equations of motion describe the flow in phase space.
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(physics) an ideal space in which the coordinate dimensions represent the variables that are required to describe a system or substance
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a multidimensional phase space
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