Ch. Gruber and J. Piasecki
Stationary Motion of the Adiabatic Piston
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ABSTRACT. 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.