Steady-State Conduction in Self-Similar Billiards

Felipe Barra and Thomas Gilbert
Phys. Rev. Lett. 98, 130601 – Published 28 March 2007

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.

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  • Received 4 October 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.130601

©2007 American Physical Society

Authors & Affiliations

Felipe Barra1 and Thomas Gilbert2

  • 1Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
  • 2Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium

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Vol. 98, Iss. 13 — 30 March 2007

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