Viscosity in the escape-rate formalism

Abstract

We apply the escape-rate formalism to compute the shear viscosity in terms of the chaotic properties of the underlying microscopic dynamics. A first passage problem is set up for the escape of the Helfand moment associated with viscosity out of an interval delimited by absorbing boundaries. At the microscopic level of description, the absorbing boundaries generate a fractal repeller. The fractal dimensions of this repeller are directly related to the shear viscosity and the Lyapunov exponent, which allows us to compute its values. We apply this method to the Bunimovich-Spohn minimal model of viscosity which is composed of two hard disks in elastic collision on a torus. These values are in excellent agreement with the values obtained by other methods such as the Green-Kubo and Einstein-Helfand formulas.

16 pages, 16 figures (accepted in Phys. Rev. E; October 2003)

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• Transport properties in chaotic and non-chaotic many particles systems
• Geometrical origin of chaoticity in the bouncing ball billiard
• Entropy production in diffusion-reaction systems: The reactive random Lorentz gas
• Random paths and current fluctuations in nonequilibrium statistical mechanics
• The entropy of co-compact open covers
• Chaoticity of the Wet Granular Gas
• Viscosity from Newton to Modern Non-equilibrium Statistical Mechanics