Viscosity in the escape-rate formalism

TL;DR

This paper uses the escape-rate formalism to connect microscopic chaotic dynamics with shear viscosity, employing fractal repellers and applying the method to a two-disk model, achieving results consistent with traditional approaches.

Contribution

It introduces a novel application of the escape-rate formalism to compute shear viscosity from microscopic chaos properties, linking fractal dimensions and Lyapunov exponents.

Findings

Viscosity values match those from Green-Kubo and Einstein-Helfand methods.

Fractal repellers are used to relate microscopic chaos to macroscopic viscosity.

Method successfully applied to a minimal two-disk model.

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.