Boundary driven shear flows and wall thermostats are being used in computer simulations of materials with increasing frequency. One attraction is that such boundary constraints offer a more realistic representation of the physical constraints imposed experimentally than the widely employed homogeneous constraints. In this paper we derive the linear response expressions for shear viscosity and thermal conductivity based on the fluctuations associated with boundary constraints. We demonstrate that our approach provides an effective method of describing the rheology in interfaces as well as bulk samples.
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