  A Lorentz gas may be defined as a system of fixed dispersing scatterers, with
a single light particle moving among these and making specular collisions on
encounters with the scatterers. For a dilute Lorentz gas with open boundaries
in $d$ dimensions we relate the thermodynamic formalism to a random flight
problem. Using this representation we analytically calculate the central
quantity within this formalism, the topological pressure, as a function of
system size and a temperature-like parameter $\ba$. The topological pressure is
given as the sum of the topological pressure for the closed system and a
diffusion term with a $\ba$-dependent diffusion coefficient. From the
topological pressure we obtain the Kolmogorov-Sinai entropy on the repeller,
the topological entropy, and the partial information dimension.
