Fluctuating hydrodynamics and irreversible thermodynamics. (Q5952834)

The equilibrium Rayleigh-Brillouin spectrum for light scattering in a viscoelastic Maxwell fluid with classical heat conduction is analized, by means of two different methods: fluctuating hydrodynamics and a procedure proposed by \textit{R. D. Mountain} [Rev. Mod. Phys. 38, 205 (1966)]. It is found that both calculations yield the same result only if the hydrodynamic noise in the former method is described by the classical Landau-Lifshitz form for a dispersive transport coefficient (in this case, shear viscosity). The result is compared with and expression of the fluctuation-dissipation theorem proposed in extended thermodynamics [\textit{D. Jou, J. Casas-Vázquez} and \textit{G. Lebon}, Extended irreversible thermodynamics. Berlin: Springer (2001; Zbl 0974.74003)], which yields, according to the authors, a result different from Mountain's one. Unfortunately, the expression (40) used by the authors for the hydrodynamic noise is not the one proposed in extended thermodynamics, in such a way that their suggestion that this theory should be modified is unfounded.