1. Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston
- Author
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Gruber, C., Pache, S., and Lesne, A.
- Subjects
Condensed Matter - Statistical Mechanics - Abstract
We investigate the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided into two chambers by a movable adiabatic piston of mass $M\gg m$. Using a two-time-scale perturbation approach in terms of the small parameter $\alpha=2m/(M+m)$, we show that the evolution towards thermal equilibrium proceeds in two stages. The first stage is a fast, deterministic, adiabatic relaxation towards mechanical equilibrium. The second stage, which takes place at times ${\cal O}(M)$, is a slow fluctuation-driven, diathermic relaxation towards thermal equilibrium. A very simple equation is derived which shows that in the second stage, the position of the piston is given by $X_M(t)=L[1/2-\xi(\alpha t)]$ where the function $\xi$ is independent of $M$. Numerical simulations support the assumptions underlying our analytical derivations and illustrate the large mass range in which the picture holds., Comment: 28 pages, 8 figures
- Published
- 2003
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