549 0022-4715/02/1100-0549/0 © 2002 Plenum Publishing Corporation Journal of Statistical Physics, Vol. 109, Nos. 3/4, November 2002 (© 2002) Strong and Weak Damping in the Adiabatic Motion of the Simple Piston G. P. Morriss 1 and Ch. Gruber 2 1 School of Physics, University of New South Wales, UNSW Sydney NSW 2052, Australia; e-mail: G.Morriss@unsw.edu.au 2 Institut de Physique Théorique, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland. Received December 20, 2001; accepted March 25, 2002 We investigate the microscopic mechanisms associated with strong and weak damping in the adiabatic motion of the simple piston with finite mass and finite amount of gas. The velocity of the piston relative to the thermal velocity of the gas particles is the principal factor in determining the behaviour. When the piston velocity is always smaller than the thermal velocity we observe weak damping. When it is greater than the thermal velocity for part of its motion there is strong damping. KEY WORDS: Damping; adiabatic; piston. 1. INTRODUCTION The ‘‘adiabatic piston’’ is a classic textbook example of a problem which can not be solved using the two laws of thermostatics. The system consists of a finite cylinder containing two gases separated by a movable adiabatic piston. Initially the two gases are in thermal equilibrium and the piston is fixed. The problem is to study the time evolution, and the final state, when the piston is free to move. (1) Recently this problem was investigated using the Boltzmann equation, (2) the Liouville equation (3) as well as using numerical simulation. It is now clear that the evolution of the piston pro- ceeds in two stages with time scales which are very different if the mass of the gas molecules is much smaller than the mass of the piston. In the first stage the evolution of the piston is deterministic and the system evolves adiabatically (no heat transfer from one gas to the other) toward a state of mechanical equilibrium (equal pressures on both sides). On the other hand