An approximate formula for the diffusion coefficient for the periodic Lorentz gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates. -- Highlights: ► An expression for the diffusion coefficient in the periodic Lorentz gas is derived. ► This simple expression compares favourable with numerical calculations. ► Approximation is superior to the Machta and Zwanzig result.