A simple piston problem in one dimension

Abstract

We study a heavy piston that separates finitely many ideal gas particles moving inside a one-dimensional gas chamber. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged behavior. The convergence is uniform over all initial conditions in a compact set. The results extend earlier work by Sinai and Neishtadt, who determined that the averaged behavior is periodic oscillation. In addition, we investigate the piston system when the particle interactions have been smoothed. The convergence to the averaged behavior again takes place uniformly, both over initial conditions and over the amount of smoothing.

Accepted by Nonlinearity. 27 pages, 2 figures

References in corpus (3)

• Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston
• On a slow drift of a massive piston in an ideal gas that remains at mechanical equilibrium
• Deterministic motion of the controversial piston in the thermodynamic limit

Cited by in corpus (7)

• Dirac structures in nonequilibrium thermodynamics
• Low stratification of a heat-conducting fluid in time-dependent domain
• On the zero mass limit of tagged particle diffusion in the 1-d Rayleigh-gas
• Rigorous Results for the Periodic Oscillation of an Adiabatic Piston
• Non-equilibrium dynamics of the piston in the Szilard engine
• Flow of heat conducting fluid in a time dependent domain
• The periodic oscillation of an adiabatic piston in two or three dimensions