On the Green-Kubo relationship for the liquid-solid friction coefficient

In this paper, we propose a new derivation for the Green-Kubo relationship for the liquid-solid friction coefficient characterizing hydrodynamic slippage at a wall. It is based on a general Langevin approach for the fluctuating wall velocity involving a non-Markovian memory kernel with vanishing time integral. The calculation highlights some subtleties of the wall-liquid dynamics leading to superdiffusive motion of the fluctuating wall position.