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About Liouville's theorem(classical mechanics)

  1. Sep 19, 2009 #1
    Here is a statement about the Liouville's theorem in my textbook:
    "Because we are unable to discuss the details of the particles' motion in the actual system, we substitute a discussion of an ensemble of equivalent systems. Each representative in the phase space corresponds to a single system of the ensemble, and the motion of a particular point represents the independent motion of that system"
    I don't understand what it means by "independent" in the last sentence, does it mean the particles are assumed not to collide with each other in the real configuration space?
  2. jcsd
  3. Sep 19, 2009 #2


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    Independent here means that the different systems in the ensemble have nothing to do with each other. The time evolution of a system in the ensemble depends only on its starting point in the phase space (and the Hamiltonian).
    Last edited: Sep 19, 2009
  4. Sep 19, 2009 #3
    So "Independent" includes the collisionless case I mentioned, or such as particles don't exert force on each other, am I correct?
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