Geodesic
Dynamics of a~massive piston in an ideal gas
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 57 (2002) no. 6, pp. 1045-1125

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This survey is a study of a dynamical system consisting of a massive piston in a cubic 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 $m=1$. It is found that under suitable initial conditions there is 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 (hydrodynamic equations) such that in the limit $L\to\infty$ the mechanical trajectory of the piston converges in probability to the solution of the hydrodynamic equations for a certain period of time. There is also a heuristic discussion of the dynamics of the system on longer intervals of time. 
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     author = {N. I. Chernov and J. L. Lebowitz and Ya. G. Sinai},
     title = {Dynamics of a~massive piston in an ideal gas},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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N. I. Chernov; J. L. Lebowitz; Ya. G. Sinai. Dynamics of a~massive piston in an ideal gas. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 57 (2002) no. 6, pp. 1045-1125. http://geodesic.mathdoc.fr/item/RM_2002_57_6_a0/