Computation of the viscosity of a liquid from time averages of stress fluctuations

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Abstract
The shear viscosity can be calculated from the standard deviation of an equilibrium ensemble of time averages of the shear stress computed along finite duration phase space trajectory segments. The mean square of the segment averages of the shear stress is proportional to the shear viscosity and inversely proportional to the duration of the trajectory segments and the number of particles. We test the fluctuation relation for the shear viscosity and show that it provides a simple but viable means of computing the zero strain rate shear viscosity. We decompose the shear viscosity computed using this fluctuation method, into its “kinetic” and “configurational” components. We also calculate the relevant relaxation times. We compare the computed results with standard nonequilibrium molecular dynamics simulations. Finally we compute the bulk viscosity using an analogous fluctuation method.