Fluctuation-dissipation theorems for viscoelastic fluids: consistency of extended thermodynamic theories

Abstract

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 .