From the definitions of R(t) and 
, it is straightforward to show that
there is a relation between them of the form
This relation is known as the second fluctuation dissipation theorem.
The fact that it involves a simple autocorrelation function of the
random force is particular to the harmonic bath model. We will see later that
a more general form of this relation exists, valid for a general bath. This
relation must be kept in mind when introducing models for R(t) and .
In effect, it acts as a constraint on the possible ways in which one can model
the random force and friction kernel.