Viscosity of a simple fluid from its maximal Lyapunov exponents

This is the authors' abstract. We don't add key points for this paper.

We compute the viscosity {η} of a fluid consisting of a large number of particles, N=108 and 864, as a function of shear rate {γ} 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 {γ} are determined using nonequilibrium molecular dynamics (NEMD) computer simulations. The {η}({γ}) computed this way agree with those obtained directly from NEMD within the experimental error of 2% for the triple-point N=108 system. A γ1/2 dependence of {η}({γ}) for large {γ} is found up to a P\'eclet number of 5.