Liouville's theorem
From SklogWiki
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 \(\varrho\) 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.
