Dissipative collapse of the adiabatic piston

– An adiabatic piston, separating two granular gases prepared in the same macro-scopic state, is found to eventually collapse to one of the sides. This new instability is explained by a simple macroscopic theory which is furthermore in qualitative agreement with hard disk molecular dynamics. The problem of the so-called adiabatic piston was described in 1960 by Callen [1] and has received a lot of attention recently [2, 3]. This construction consists of a cylinder containing two gases separated by an adiabatic piston. It is of interest because the principle of maximum entropy does not predict the equilibrium state [1, 2]. In particular any state with gases left and right at equilibrium with the same pressure is a possible equilibrium state of the compound system, even if the gases are at different temperatures. The degeneracy is however lifted when one moves away from the macroscopic limit. When fluctuations are taken into account, the setup becomes a Brownian motor [4] and the piston moves towards the cold chamber until the system relaxes to " full " equilibrium with equal temperatures and pressures in both gases. In this letter, we raise a different question: what happens when the gases are granular, i.e., they gradually loose energy due to dissipative collisions. Our motivation is twofold. On the one hand, granular matter has recently been the object of intensive theoretical and experimental research [5]. Somewhat surprisingly, freely moving boundaries, which can be easily realized in experiment, have not received much attention. On the other hand, we will show that the situation is in a sense more dramatic than in the above mentioned non-dissipative case. Of particular interest to us is the case when both gases are prepared in the same macroscopic state. One expects that the piston will not move because of the left-right symmetry, which is preserved as the gases cool on both sides by dissipative collisions. However, our analysis will reveal that this state is unstable. Fluctuations or small disturbances will induce a motion of the piston which amplifies and finally leads to a full collapse of one of the gases. The origin