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theorems:liouvilles_theorem

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theorems:liouvilles_theorem [2018/07/04 13:20]
jakobadmin [Concrete]
theorems:liouvilles_theorem [2019/03/05 14:07] (current)
129.13.36.189 [Concrete]
Line 113: Line 113:
 $$\frac{\partial \rho }{\partial t}= -\sum_{i}\left(\frac{\partial \rho}{\partial q_i}\,​\dot{q_i}+\frac{\partial\rho}{\partial p_i}\,\dot p_i\right).$$ $$\frac{\partial \rho }{\partial t}= -\sum_{i}\left(\frac{\partial \rho}{\partial q_i}\,​\dot{q_i}+\frac{\partial\rho}{\partial p_i}\,\dot p_i\right).$$
  
-This is a dynamical equation for the time-evolution of $\rho(t,​\vec p,\vec q)$ that follows when the flow of the probability density $\rho(t,​\vec p,\vec q)$ is incompressible,​ i.e. $\frac{\partial ​\rho }{\partial ​t}= 0$.+This is a dynamical equation for the time-evolution of $\rho(t,​\vec p,\vec q)$ that follows when the flow of the probability density $\rho(t,​\vec p,\vec q)$ is incompressible,​ i.e. $\frac{\rho }{t}= 0$.
  
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theorems/liouvilles_theorem.txt · Last modified: 2019/03/05 14:07 by 129.13.36.189