Steady-state conduction in self-similar billiards

Details Steady-state conduction in self-similar billiards Steady-state conduction in self-similar billiards

2007-05-18

arxiv.org/abs/0705.2758v1

Physical Review Letters vol, 98, 130601 (2007)

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevLett.98.130601

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 monotonically according to their indices. This special geometry induces a nonequilibrium 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.

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