Fluctuation-dissipation theorems in the GENERIC formalism: The viscoelastic fluids

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. The FDR exhibits specific features arising from the type of entropy used in the formalism but the understanding of fluctuations in a given non-equilibrium system is reduced to determining a single friction matrix. We show that consistent results with fundamental laws of irreversible thermodynamics for Maxwell fluid are obtained if it is used the corresponding entropy in LIT. If structural properties of the fluid are used as thermodynamic variables, giving rise to extended irreversible thermodynamics, the resulting FDR also shows the desired properties. We discuss these results under the scope of the relation among levels of description and statistical properties of fluctuating thermodynamic fields.