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Adiabatic piston in a temperature gradient

The steady states of two gases of hard spheres or disks separated by an adiabatic piston in presence of a temperature gradient are discussed. The temperature field is generated by two thermal walls at different temperatures, each of them in contact with one of the gases. The presence of the piston strongly affects the hydrodynamic fields, inducing a jump in its vicinity. A simple kinetic theory model is formulated. Its predictions are shown to be in good agreement with molecular dynamics simulation results. The applicability of the minimum entropy production principle is analyzed, and it is found that it only provides an accurate description of the system in the limit of a small temperature gradient.