Derivation of Stokes' Law from Kirkwood's Formula and the Green-Kubo Formula via Large Deviation Theory

摘要

We study the friction coefficient of a macroscopic sphere in a viscous fluidat low Reynolds number. First, Kirkwood's formula for the friction coefficientis reviewed on the basis of the Hamiltonian description of particle systems.According to this formula, the friction coefficient is expressed in terms ofthe stress correlation on the surface of the macroscopic sphere. Then, with theaid of large deviation theory, we relate the surface stress correlation to thestress correlation in the bulk of the fluid, where the latter is characterizedby the viscosity in the Green-Kubo formula. By combining Kirkwood's formula andthe Green-Kubo formula in large deviation theory, we derive Stokes' law withoutexplicitly employing the hydrodynamic equations.