Fourier's Law in a Generalized Piston Model

Abstract

A simplified, but non trivial, mechanical model -- gas of $N$ particles of mass $m$ in a box partitioned by $n$ mobile adiabatic walls of mass $M$ -- interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantities for the stationary non-equilibrium states. The results are compared with extensive numerical simulations; in the limit of large $n$, $mN/M\gg 1$ and $m/M\ll 1$, we find a good approximation of Fourier's law.

arXiv comment14 pages, 5 figures

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Cited by in corpus (3)

• Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory
• Mesoscopic description of the adiabatic piston: kinetic equations and $\mathcal{H}$-theorem
• Effective Langevin equations leading to large deviation function of time-averaged velocity for a nonequilibrium Rayleigh piston