Stationary motion of the adiabatic piston

We consider a one-dimensional system consisting of two infinite ideal fluids, with equal pressures but different temperatures T1 and T2, separated by an adiabatic movable piston whose mass M is much larger than the mass m of the fluid particles. This is the infinite version of the controversial adiabatic piston problem. The stationary non-equilibrium solution of the Boltzmann equation for the velocity distribution of the piston is expressed in powers of the small parameter , and explicitly given up to order ε2. In particular it implies that although the pressures are equal on both sides of the piston, the temperature difference induces a non-zero average velocity of the piston in the direction of the higher temperature region. It thus shows that the asymmetry of the fluctuations induces a macroscopic motion despite the absence of any macroscopic force. This same conclusion was previously obtained for the non-physical situation where M=m