Time correlation functions in the stress ensemble

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Abstract
In this paper we derive a complete set of equilibrium fluctuation relations for the frequency dependent shear viscosity in ensembles in which the shear stress is the independent thermodynamic state variable. To date all such fluctuation relations, the so-called Green-Kubo relations, have been restricted to ensembles in which the strain rate is the independent variable. Our relations show how the frequency dependent viscosity can be calculated from either the strain rate or the stress fluctuations present in a system maintained at a fixed average shear stress. Our relations are tested against NEMD computer experiments and found to be consistent with the numerical data.