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I General Boltzmann equation

  1. Dec 6, 2017 #1
    I've seen the derivation where:

    ## \frac {df}{dt} = \frac {\partial f}{\partial t} + \vec {v} \cdot \vec {\nabla} f + \vec {a} \cdot \vec \nabla_{\vec{v}} f ##

    Although I was told this should more generally be written as:

    ## \frac {df}{dt} = \frac {\partial f}{\partial t} + \vec {\nabla} \cdot ({ {\vec {v}}} f) + \vec {\nabla}_{{\vec{v}}} \cdot ({{\vec {a}}} f) ##

    Which follows straightforwardly from the first expression if velocity is independent of position and acceleration is independent of velocity. But would you happen to know where I can find the derivation for the latter expression more generally from first principles (as shown for the first expression)?
  2. jcsd
  3. Dec 11, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
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