Liouville's theorem
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Liouville's theorem is an expression of the conservation of volume of phase space:
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\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 (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \varrho} is a distribution function Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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.