  The time evolution of the adiabatic piston problem and the consequences of
its stochastic motion are investigated. The model is a one dimensional piston
of mass $M$ separating two ideal fluids made of point particles with mass $m\ll
M$. For infinite systems it is shown that the piston evolves very rapidly
toward a stationary nonequilibrium state with non zero average velocity even if
the pressures are equal but the temperatures different on both sides of the
piston. For finite system it is shown that the evolution takes place in two
stages: first the system evolves rather rapidly and adiabatically toward a
metastable state where the pressures are equal but the temperatures different;
then the evolution proceeds extremely slowly toward the equilibrium state where
both the pressures and the temperatures are equal. Numerical simulations of the
model are presented. The results of the microscopical approach, the
thermodynamical equations and the simulations are shown to be qualitatively in
good agreement.
