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We study the periodic Lorentz gas in the Boltzmann-Grad limit, whoseconvergence was rigorously established in the seminal work ofMarklof-Str\"ombergsson. Extending the two dimensional results ofBoca-Zaharescu to higher dimensions, we present a more detailed description ofthis convergence. More precisely, we derive the asymptotic formula of thedistribution function of the free path length; and we explicitly compute theconstant in the asymptotic formula for the Kolmogorov-Sinai (K-S) entropy ofthe billiard map.

The periodic Lorentz gas in the Boltzmann-Grad limit: the free path length and the K-S entropy