THE WIND-ROUND-TREE MODEL AND THE 2-DIMENSIONAL LORENTZ GAS

In this Letter we establish the equivalence of the two-dimensional non overlapping Lorentz gas and the Ehrenfests' wind-tree model considerin g round (instead of square) trees. To obtain the Boltzmann equation fo r this latter model we use the infinite polygonal limit which turns ou t to be smooth and continuous. Finally we present the general solution of the Boltzmann equation which provides a simple discussion on the e rgodicity of the model.