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A Lorentz gas may be defined as a system of fixed dispersing scatterers, witha single light particle moving among these and making specular collisions onencounters with the scatterers. For a dilute Lorentz gas with open boundariesin $d$ dimensions we relate the thermodynamic formalism to a random flightproblem. Using this representation we analytically calculate the centralquantity within this formalism, the topological pressure, as a function ofsystem size and a temperature-like parameter $\ba$. The topological pressure isgiven as the sum of the topological pressure for the closed system and adiffusion term with a $\ba$-dependent diffusion coefficient. From thetopological pressure we obtain the Kolmogorov-Sinai entropy on the repeller,the topological entropy, and the partial information dimension.Comment: 7 pages, 5 figure

physical review. e, statistical, nonlinear and soft matter physics

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Thermodynamic formalism for the Lorentz gas with open boundaries inddimensions