Viscosity in the escape-rate formalism

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.