Heat conduction and entropy production in a one-dimensional hard-particle gas

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses and correct several claims in recent literature based on much smaller simulations. We find heat conductivities kappa to diverge with the number N of particles. These depended strongly on the mass ratio, and extrapolations to N--> infinity, and t--> infinity, are difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa approximately N(alpha) with alpha approximately 0.33 suggesting a relation to the Kardar-Parisi-Zhang model. We finally discuss why the system leads nevertheless to energy dissipation and entropy production, in spite of not being chaotic in the usual sense.