Steady-state conduction in self-similar billiards
Chaotic Dynamics
2009-11-13 v1
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 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.
Cite
@article{arxiv.0705.2758,
title = {Steady-state conduction in self-similar billiards},
author = {Felipe Barra and Thomas Gilbert},
journal= {arXiv preprint arXiv:0705.2758},
year = {2009}
}