Editing 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  <math>\Gamma</math>-space, is an Euclidean space in <math>2s</math> dimensions 
(''i.e.'' <math>E^{2s}</math>), where <math>s</math>
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 (known as a ''phase point''). Changes in the system now trace out a trajectory
in phase space (known as a ''phase trajectory''). 
Two different phase trajectories cannot pass through the same phase point.
One important property 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]]
[[category: statistical mechanics]]