One dimensional Brownian motion in hard rods: adiabatic piston problem

TL;DR

This study examines the dynamics of a piston in a one-dimensional hard-rod gas, revealing oscillatory behavior, diffusion characteristics, and equilibrium properties through molecular dynamics simulations.

Contribution

It provides analytical and simulation-based insights into the piston’s motion and diffusion in a 1D hard-rod system without thermal noise, highlighting its oscillatory and equilibrium behavior.

Findings

Piston exhibits oscillations with decaying amplitude before reaching equilibrium.

Analytical expressions for the piston’s mean-squared displacement are derived.

Piston’s MSD is similar to that of normal rods despite larger mass and size.

Abstract

We have investigated the motion characteristics of a movable piston immersed in a one dimensional gas of hard rods by event-oriented molecular dynamics in the absence of thermal noise. Periodic and reflecting boundary conditions are explored. It is shown that the piston undergoes systematic oscillations with decaying amplitudes in short times before it comes to global thermodynamic equilibrium. Moreover, the diffusion of the piston is explored and analytical expressions for its equilibrium mean-squared displacement is obtained. It is shown that MSD of the piston does not differ much from the normal rods despite its mass and length are significantly larger.