Viscous flow in the stress ensemble

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Abstract
The stress ensemble has advantages for studying shear flow in highly viscous media. We derive a simple method for performing nonequilibrium molecular dynamics simulations in this ensemble. We also derive the associated equilibrium fluctuation expressions for the zero frequency shear viscosity. These expressions relate the reciprocal of the shear viscosity to strain rate fluctuations in the zero stress equilibrium ensemble. Our analysis is based upon the Nosé-Hoover method of treating non-holonomic constraints. We show that for generating the stress ensemble, the Nosé-Hoover method is much simpler to implement than the corresponding gaussian approach.