  We consider a classical model of non-equilibrium statistical mechanics
accounting for non-Markovian effects, which is referred to as the Generalized
Langevin Equation in the literature. We derive reduced Markovian descriptions
obtained through the neglection of inertial terms and/or heat bath variables.
The adopted reduction scheme relies on the framework of the Invariant Manifold
method, which allows to retain the slow degrees of freedom from a multiscale
dynamical system. Our approach is also rooted on the Fluctuation-Dissipation
Theorem, which helps preserve the proper dissipative structure of the reduced
dynamics. We highlight the appropriate time scalings introduced within our
procedure, and also prove the commutativity of selected reduction paths.
