Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston

Details Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston

2003-12-13

arxiv.org/abs/cond-mat/0312339v1

Journal of Statistical Physics, 112, 1199-1228 (2003)

Physics

Condensed Matter

Statistical Mechanics

28 pages, 8 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-580478