  We determine the nonlocal stress autocorrelation tensor in an homogeneous and
isotropic system of interacting Brownian particles starting from the
Smoluchowski equation of the configurational probability density. In order to
relate stresses to particle displacements as appropriate in viscoelastic
states, we go beyond the usual hydrodynamic description obtained in the
Zwanzig-Mori projection operator formalism by introducing the proper
irreducible dynamics following Cichocki and Hess, and Kawasaki. Differently
from these authors, we include transverse contributions as well. This recovers
the expression for the stress autocorrelation including the elastic terms in
solid states as found for Newtonian and Langevin systems, in case that those
are evaluated in the overdamped limit. Finally, we argue that the found memory
function reduces to the shear and bulk viscosity in the hydrodynamic limit of
smooth and slow fluctuations and derive the corresponding hydrodynamic
equations.
