Editing Phase space (section)

{{Use American English|date=January 2019}}
{{Use mdy dates|date=January 2019}}
{{Short description|Space of all possible states that a system can take}}
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[[File:Simple Harmonic Motion Orbit.gif|right|thumb|upright=1.5|Diagram showing the periodic orbit of a mass-spring system in [[simple harmonic motion]]. (The velocity and position axes have been reversed from the standard convention in order to align the two diagrams)]]
{{Differential equations}}

The '''phase space''' of a [[physical system]] is the set of all possible [[State (disambiguation)|physical states]] of the system when described by a given parameterization. Each possible state corresponds uniquely to a [[point (geometry)|point]] in the phase space. For [[classical mechanics|mechanical systems]], the phase space usually consists of all possible values of the [[position (vector)|position]] and [[momentum]] parameters. It is the [[direct product]] of direct space and [[reciprocal space]].{{unclear-inline|date=March 2023}} The concept of phase space was developed in the late 19th century by [[Ludwig Boltzmann]], [[Henri Poincaré]], and [[Josiah Willard Gibbs]].<ref>{{Cite journal | last1 = Nolte | first1 = D. D. | title = The tangled tale of phase space | doi = 10.1063/1.3397041 | journal = Physics Today | volume = 63 | issue = 4 | pages = 33–38| year = 2010 |bibcode = 2010PhT....63d..33N | s2cid = 17205307 }}</ref>