Nonequilibrium Statistical Mechanics for Adiabatic Piston Problem

Abstract

We consider the dynamics of a freely movable wall of mass $M$ with one degree of freedom that separates a long tube into two regions, each of which is filled with rarefied gas particles of mass $m$. The gases are initially prepared at equal pressure but different temperatures, and we assume that the pressure and temperature of gas particles before colliding with the wall are kept constant over time in each region. We elucidate the energetics of the setup on the basis of the local detailed balance condition, and then derive the expression for the heat transferred from each gas to the wall. Furthermore, by using the condition, we obtain the linear response formula for the steady velocity of the wall and steady energy flux through the wall. Using perturbation expansion in a small parameter $\epsilon \equiv \sqrt{m/M}$, we calculate the steady velocity up to order $\epsilon$.

17 pages, 2 figures

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• Intrinsic ratchets: A Hamiltonian approach
• Archimedes' principle for ideal gas
• Efficiency at maximum power output for an engine with a passive piston
• Multiplicative Langevin Equation to Reproduce Long-time Properties of Nonequilibrium Brownian Motion
• Effective Langevin equations leading to large deviation function of time-averaged velocity for a nonequilibrium Rayleigh piston