  We consider a system of interacting particles governed by the generalized
Langevin equation (GLE) in the presence of external confining potentials,
singular repulsive forces, as well as memory kernels. Using a Mori-Zwanzig
approach, we represent the system by a class of Markovian dynamics. Under a
general set of conditions on the nonlinearities, we study the large-time
asymptotics of the multi-particle Markovian GLEs. We show that the system is
always exponentially attractive toward the unique invariant Gibbs probability
measure. The proof relies on a novel construction of Lyapunov functions. We
then establish the validity of the small mass approximation for the solutions
by an appropriate equation on any finite-time window. Important examples of
singular potentials in our results include the Lennard-Jones and Coulomb
functions.
