From the adiabatic piston to macroscopic motion induced by fluctuations

The controversial problem of the evolution of an isolated system with an in ternal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-di mensional ideal fluids separated by a piston whose mass is equal to the mas s of the fluid particles we obtain a rigorous explicit stationary non-equil ibrium solution of the Boltzmann equation. It is shown that at equal pressu res on both sides of the piston, the temperature difference induces a non-z ero 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 remarkabl e effect is analogous to the dynamics of stochastic ratchets, where fluctua tions conspire with spatial anisotropy to generate directed motion. However , a different mechanism is involved here. The relevance of the discovered m otion to the adiabatic piston problem is discussed. (C) 1999 Elsevier Scien ce B.V. All rights reserved.