Dynamics of a Massive Piston in an Ideal Gas: Oscillatory Motion and Approach to Equilibrium

Details Dynamics of a Massive Piston in an Ideal Gas: Oscillatory Motion and Approach to Equilibrium Dynamics of a Massive Piston in an Ideal Gas: Oscillatory Motion and Approach to Equilibrium

2002-12-30

arxiv.org/abs/cond-mat/0212638v1

Journal of Statistical Physics, volume 109, 2002, pp. 507-527

Physics

Condensed Matter

Statistical Mechanics

19 pages, 9 figures

Scientific paper

We study numerically and theoretically (on a heuristic level) the time evolution of a gas confined to a cube of size $L^3$ divided into two parts by a piston with mass $M_L \sim L^2$ which can only move in the $x$-direction. Starting with a uniform ``double-peaked'' (non Maxwellian) distribution of the gas and a stationary piston, we find that (a) after an initial quiescent period the system becomes unstable and the piston performs a damped oscillatory motion, and (b) there is a thermalization of the system leading to a Maxwellian distribution of the gas velocities. The time of the onset of the instability appears to grow like $L \log L$ while the relaxation time to the Maxwellian grows like $L^{7/2}$.

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