Fourier's Law in a Generalized Piston Model

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 >> 1 and m/M << 1, we find a good approximation of Fourier's law.