  The fluctuation-dissipation theorem (FDT) is very general and applies to a
broad variety of different physical phenomena in condensed matter physics. With
the help of the FDT and following the famous work of Caldeira and Leggett, we
show that, whenever linear response theory applies, any generic bosonic or
fermionic system at finite temperature $T$ can be mapped onto a fictitious
system of free harmonic oscillators. To the best of our knowledge, this is the
first time that such a mapping is explicitly worked out. This finding provides
further theoretical support to the phenomenological harmonic oscillator models
commonly used in condensed matter. Moreover, our result helps in clarifying an
interpretation issue related to the presence and physical origin of the
Bose-Einstein factor in the FDT.
