Kinetic equations, initial conditions and time-reversal: A solvable one-dimensional model revisited

We present a detailed analysis of the kinetic behaviour of a one-dimensional Rayleigh model, consisting of one hard point interacting with otherwise freely moving points. We generalized the previous work of Jepsen and others by taking into account initial correlations between the particles; we are also able to make precise statements about the role of the thermodynamic limit and the meaning of molecular chaos - and its persistence -. Finally, we show that our kinetic description satisfies the requirements of time reversal. Except for a few mathematical assumptions, our calculations involve no approximation.