N. Chernov, J. L. Lebowitz, Ya. Sinai
Dynamics of a Massive Piston in an Ideal Gas
(794K, PDF)

ABSTRACT.  We study a dynamical system consisting of a massive piston in a 
cubical container of large size $L$ filled with an ideal gas. The 
piston has mass $M\sim L^2$ and undergoes elastic collisions with 
$N\sim L^3$ non-interacting gas particles of mass $m=1$. We find 
that, under suitable initial conditions, there is, in the limit $L 
\to \infty$, a scaling regime with time and space scaled by $L$, 
in which the motion of the piston and the one particle 
distribution of the gas satisfy autonomous coupled equations 
(hydrodynamical equations), so that the mechanical trajectory of 
the piston converges, in probability, to the solution of the 
hydrodynamical equations for a certain period of time. We also 
discuss heuristically the dynamics of the system on longer 
intervals of time.