I am studying about the Boltzmann Equation for non-equilibrium rarefied gases (dilute gases to be more specific): $$\frac{\partial f}{\partial t}+\pmb{v}\cdot\nabla_{\pmb{x}}f=Q(f,f)$$

My question is this: is the Maxwell distribution a solution of the equation above?

  • 2
    $\begingroup$ Yes, it is a global and local sulution. $\endgroup$
    – Hydro Guy
    Mar 17, 2015 at 12:17

1 Answer 1


It has to be, because the Maxwell-Boltzmann distribution is the maximum entropy distribution. If your model does not allow relaxation to the Maxwell-Boltzmann distribution it is in conflict with the second law of thermodynamics.


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