Liouville's theorem

Liouville's theorem is an expression of the conservation of volume of phase space:

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

where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \varrho } is a distribution function $\varrho (p,q)$, p is the generalised momenta and q are the generalised coordinates. With time a volume element can change shape, but phase points neither enter nor leave the volume.