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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?
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.
