We do not solve the transport equation here. But to illustrate the kind of processes it can describe, we simulate a 2-dimensional system of hard discs in a rectangular box. At the start all particles are in the left part of the container; their velocities are randomly chosen (not from a Maxwell-Boltzmann distribution). This nonequilibrium state is not stable, and in time the particles will fill the entire box in a (statistically) homogeneous way: approach to equilibrium.
The nobs on the wall are not necessary, but they speed up the mixing of velocities.
[Code: BM]

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