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phase space


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For a system with n degrees of freedom, the 2n-dimensional space with coordinates (q1, q2, …, qn, p1, p2, …, pn), where the qs describe the degrees of freedom of the system and the ps are the corresponding momenta. Each point represents a state of the system. In a gas of N point particles, each particle has three positional coordinates and three corresponding momentum coordinates, so that the phase space has 6N-dimensions. If the particles have internal degrees of freedom, such as the vibrations and rotations of molecules, then these must be included in the phase space, which is consequently of higher dimension than that for point particles. As the system changes with time the representative points trace out a curve in phase space known as a trajectory. See also attractor; configuration space; statistical mechanics.

Subjects: Earth Sciences and Geography — Chemistry.


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