Unifying renormalized and bare viscosity in two-dimensional molecular dynamics simulations

Fluctuating hydrodynamics provides a framework connecting mesoscopic fluctuations with macroscopic transport behavior. To bridge mesoscopic and macroscopic transport from microscopic dynamics, we introduce a wave-number-dependent viscosity, defined via the equilibrium correlation of time-averaged Fourier components of the fine-grained shear stress field. Two-dimensional molecular dynamics simulations reveal its small-wave-number divergence characteristic of the renormalized viscosity, while its large-wave-number behavior determines the bare viscosity, thereby establishing a link between mesoscopic and macroscopic transport based on microscopic dynamics.