Liouville's theorem

${\frac {d\varrho }{dt}}=\sum _{i=1}^{s}\left({\frac {\partial \varrho }{\partial q_{i}}}{\dot {q_{i}}}+{\frac {\partial \varrho }{\partial p_{i}}}{\dot {p_{i}}}\right)=0$

where $\varrho$ is a distribution function $\varrho (p,q)$, p is the generalised momenta and q are the generalised coordinates.

See also

• Phase space