General theory of the viscosity of liquids and solids from nonaffine particle motions

A microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of nonaffine linear response theory. This formula may lead to a valid alternative to the Green-Kubo approach to describe the viscosity of condensed matter systems from molecular simulations without having to fit long-time tails. Furthermore, it provides a direct link between the viscosity, the vibrational density of states of the system, and the zero-frequency limit of the memory kernel. Finally, it provides a microscopic solution to Maxwell's interpolation problem of viscoelasticity by naturally recovering Newton's law of viscous flow and Hooke's law of elastic solids in two opposite limits.