Editing Liouville's theorem
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'''Liouville's theorem''' is an expression of the conservation of volume of [[phase space]] | {{Stub-general}} | ||
'''Liouville's theorem''' is an expression of the conservation of volume of [[phase space]]: | |||
:<math>\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 </math> | :<math>\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 </math> | ||
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With time a volume element can change shape, but phase points neither enter nor leave the volume. | With time a volume element can change shape, but phase points neither enter nor leave the volume. | ||
==References== | ==References== | ||
#[http://portail.mathdoc.fr/cgi-bin/jmpar.py?O=16382&E=00000350&N=8&CD=0&F=PDF J. Liouville "Note sur la Théorie de la Variation des constantes arbitraires", Journal de Mathématiques Pures et Appliquées, Sér. I, '''3''' pp. 342-349 (1838)] | |||
[[category: statistical mechanics]] | [[category: statistical mechanics]] | ||