  We present a detailed study of the first simple mechanical system that shows
fully realistic transport behavior while still being exactly solvable at the
level of equilibrium statistical mechanics. The system under consideration is a
Lorentz gas with fixed freely-rotating circular scatterers interacting with
point particles via perfectly rough collisions. Upon imposing a temperature
and/or a chemical potential gradient, a stationary state is attained for which
local thermal equilibrium holds for low values of the imposed gradients.
Transport in this system is normal, in the sense that the transport
coefficients which characterize the flow of heat and matter are finite in the
thermodynamic limit. Moreover, the two flows are non-trivially coupled,
satisfying Onsager's reciprocity relations to within numerical accuracy as well
as the Green-Kubo relations . We further show numerically that an applied
electric field causes the same currents as the corresponding chemical potential
gradient in first order of the applied field. Puzzling discrepancies in higher
order effects (Joule heating) are also observed. Finally, the role of entropy
production in this purely Hamiltonian system is shortly discussed.
