Abstract
The self-similar Lorentz billiard channel is a spatially extended
deterministic dynamical system which consists of an infinite
one-dimensional sequence of cells whose sizes increase monotonously
according to their indices. This special geometry induces a non-equilibrium
stationary state with particles flowing steadily from the small to the
large scales. The corresponding invariant measure has fractal properties
reflected by the phase-space contraction rate of the
dynamics restricted to a single cell with appropriate boundary conditions. In
the near-equilibrium limit, we find numerical agreement
between this quantity and the entropy production rate as specified by
thermodynamics. A relation to the iso-kinetic Lorentz gas is discused.
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