Relationship between McQuarrie and Helfand equations for the determination of shear viscosity from equilibrium molecular dynamics

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Abstract
A proof of the validity of the Chialvo-Debenedetti conjecture [Phys. Rev. A 43, 4289 (1991)], the crucial element to achieve an equivalence between the McQuarrie [Statistical Mechanics (Harper & Row, New York, 1976)] and Helfand [Phys. Rev. 119, 1 (1960)] shear-viscosity equations, is presented here. Some theoretical consequences of that validity are also discussed, such as the unification of most shear-viscosity expressions into one given by Andrews for first-order transport coefficients [J. Chem. Phys. 47, 3161 (1967)]. The system-size dependence of the McQuarrie shear-viscosity values is analyzed and an extrapolation method is proposed and tested to determine the asymptotic values.