  The question of the "physical meaning" and "origin" of the Bose-Einstein (BE)
factor in the fluctuation-dissipation theorem (FDT) is often raised and this
term is sometimes interpreted as originating from a real harmonic oscillator
composition of the physical system. Such an interpretation, however, is not
really founded. Inspired by the famous work of Caldeira and Leggett, we have
been able to show that, whenever linear response theory is applicable, which is
the main hypothesis under which the FDT is established, any generic bosonic
and/or fermionic system at temperature $T$ can be mapped onto a fictitious
system of harmonic oscillators so that the suscettivity and the mean square of
the fluctuating observable of the real system coincide with the corresponding
quantities of the fictitious one. We claim that it is in this sense, and only
in this sense, that the BE factor can be interpreted in terms of harmonic
oscillators, no other physical meaning can be superimposed to it. At the best
of our knowledge, this is the first time that such a mapping is explicitly
worked out.
