  Fluctuation-Dissipation Relations (FDR) for a Maxwell fluid are computed via
the GENERIC formalism. This formalism is determined by four building blocks,
two ``potentials'' (total energy and entropy) and two ``matrices'' which
determine the dynamics, but the understanding of fluctuations in a given
non-equilibrium system is reduced to determining a single friction matrix. The
FDR exhibits interesting features, arising from the type of entropy used in the
formalism. We show explicitly this dependence FDR-Entropy, also we show that
GENERIC renders results consistent with irreversible linear thermodynamics
(TIL) \emph{only} if it is used the corresponding entropy. An inconsistent
result is provided by GENERIC when it is used a modified entropy .
