J. Piasecki and Ch. Gruber
>From the adiabatic piston to macroscopic motion
induced by fluctuations
(190K, LATeX)
ABSTRACT. The controversial problem of the evolution of an isolated system with an
internal adiabatic wall is investigated with the use of a simple
microscopic model and the Boltzmann equation. In the case of two infinite
volume
one-dimensional ideal fluids separated by a piston whose mass is equal to
the mass of the fluid particles we obtain a rigorous explicit stationary
non-equilibrium solution of the Boltzmann equation. It is shown that
at equal pressures on both sides of the piston, the temperature difference
induces a non-zero average velocity, oriented toward the region of higher
temperature. It thus turns out that despite the absence of macroscopic forces
the asymmetry of fluctuations results in a systematic macroscopic motion.
This remarkable effect is analogous to the dynamics of stochastic ratchets,
where fluctuations conspire with spatial anisotropy to generate directed
motion. However, a different mechanism is involved here. The relevance of
the discovered motion to the adiabatic piston problem is discussed.