Dynamics of a massive piston in an ideal gas: Oscillatory motion and approach to equilibrium

We study numerically and theoretically ( on a heuristic level) the time evolution of a gas confined to a cube of size L-3 divided into two parts by a piston with mass M-L similar to L-2 which can only move in the x-direction. Starting with a uniform ' ' double- peaked' ' (non Maxwellian) distribution of the gas and a stationary piston, we find that (a) after an initial quiescent period the system becomes unstable and the piston performs a damped oscillatory motion, and (b) there is a thermalization of the system leading to a Maxwellian distribution of the gas velocities. The time of the onset of the instability appears to grow like L log L while the relaxation time to the Maxwellian grows like L log L.