Phase space

Phase space is the name given to a coordinate-momentum space. It is the means by which a mechanical problem can be converted in to a geometrical problem. Phase space, sometimes written as $\mathrm{\Gamma }$-space, is an Euclidean space in $2s$ dimensions (i.e. $E^{2s}$), where $s$ is the number of degrees of freedom. Thus a description of a system in terms of positions and velocities now becomes a point in phase space. Changes in the system now trace out a trajectory in phase space.

One of the most important properties of phase space is that, for a long period of time, the phase-trajectory will spend an equal amount of time in equal volume elements.

See also

• Liouville's theorem
• H-theorem