phase space

"Phase space" is a foundational concept in various scientific fields for analyzing and visualizing the states and behaviors of complex systems.

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Definition

C1Mathematics and Physics

(technical, academic)A multidimensional space representing all possible states of a system, where each point corresponds to a unique state defined by parameters like position and momentum.

Example

  • In classical mechanics, a phase space diagram can illustrate the motion of a particle over time.
  • The concept of phase space is essential for understanding the behavior of dynamical systems.

C2Dynamical Systems Theory

(technical, academic)A geometric space containing all possible trajectories of a system, with each point representing a unique state and trajectories depicted as curves.

Example

  • In dynamical systems, the evolution of the system is visualized as a trajectory in phase space.
  • Analyzing the phase space of a system helps in predicting its future behavior.

C2Statistical Mechanics

(technical, academic)A high-dimensional space describing possible microstates of a thermodynamic system, where each point represents a unique particle configuration.

Example

  • The distribution of particles in phase space provides insights into the thermodynamic properties of the system.
  • In statistical mechanics, phase space helps in calculating the probabilities of different microstates.

Similar

Terms that have similar or relatively close meanings to "phase space":

factor spacedual spacehalf spacephase diagramdanger spacefree spacejoint space