Viscosity of a simple fluid from its maximal Lyapunov exponents

We compute the viscosity of a fluid consisting of a large number of particles, N=108 and 864, as a function of shear rate from its maximum and minimum Lyapunov exponents. The calculation is based on an extension of Smale's pairing rule of Lyapunov exponents for Hamiltonian systems to non-Hamiltonian systems in contact with a heat bath. The numerical values of these maximal Lyapunov exponents as a function of are determined using nonequilibrium molecular dynamics (NEMD) computer simulations. The () computed this way agree with those obtained directly from NEMD within the experimental error of 2% for the triple-point N=108 system. A ^1/2 dependence of () for large is found up to a P\'eclet number of 5.