Liouville's theorem: Difference between revisions
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Carl McBride (talk | contribs) (New page: :<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> where <math>\varrho</...) |
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'''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> | ||
where <math>\varrho</math> is a distribution function <math>\varrho(p,q)</math>, ''p'' is the generalised momenta and ''q'' are the | where <math>\varrho</math> is a distribution function <math>\varrho(p,q)</math>, ''p'' is the generalised momenta and ''q'' are the | ||
generalised coordinates. | generalised coordinates. | ||
==References== | ==References== | ||
[[category: statistical mechanics]] | [[category: statistical mechanics]] | ||
Revision as of 12:17, 3 August 2007
Liouville's theorem is an expression of the conservation of volume of phase space:
where is a distribution function , p is the generalised momenta and q are the generalised coordinates.
