The periodic oscillation of an adiabatic piston in two or three dimensions

Abstract

We study a heavy piston of mass $M$ that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system's averaged equation and showed that its solutions oscillate periodically. Using averaging techniques, we prove that the actual motions of the piston converge in probability to the predicted averaged behavior on the time scale $M^ {1/2} $ when $M$ tends to infinity while the total energy of the system is bounded and the number of gas particles is fixed.