  We consider a one-dimensional system consisting of two infinite ideal fluids,
with equal pressures but different temperatures T_1 and T_2, separated by an
adiabatic movable piston whose mass M is much larger than the mass m of the
fluid particules. 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 \epsilon=\sqrt{m/M}, and explicitly given up to order
\epsilon^2. 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.
