N. Chernov and J.L. Lebowitz
Dynamics of a Massive Piston in an Ideal Gas: Oscillatory Motion
and Approach to Equilibrium
(1258K, Postscript)
ABSTRACT. 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 $M_L \sim L^2$ 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 $L^{7/2}$.