Dynamics of a massive piston in an ideal gas

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 ∼ L² and undergoes elastic collisions with N ∼ L³ 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 → ∞ 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.