Hard rod hydrodynamics and the Lévy Chentsov field

We study the hydrodynamics of the hard rod model proposed by Boldrighini, Dobrushin and Soukhov by describing the displacement of each quasiparticle with respect to the corresponding ideal gas particle as a height difference in a related field. Starting with a family of nonhomo- geneous Poisson processes contained in the position-velocity-length space R3, we show laws of large numbers for the quasiparticle positions and the length fields, and the joint convergence of the quasiparticle fluctuations to a Lévy Chentsov field. We allow variable rod lengths, including negative lengths.