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Question about the evolution of an ensemble with non hamiltonian equation of motion

  1. Mar 27, 2009 #1
    Consider an ensemble of one particle systems each evolving in one spatial dimension according to the non Hamiltonian equation of motion:
    dx/dt=-ax

    where x(t) is the position of the particle at time t and a is a constant. The compressibility of this system is nonzero so the ensemble’s distribution function f(x,t) satisfies a Liouville equation of the form:
    df/dt-ax(df/fx)=af

    Where it was found that the distribution function in the form of
    f(x,t)=exp(at)*exp(-c((x^2)*exp(2at)))
    I need to describe the evolution of the ensemble distribution qualitatively and explain why it should evolve that way!
    We can see that at t=0 it's acts like a regular gaussian.

    Please help!
     
  2. jcsd
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