Fluctuations and stochastic noise in systems with hyperbolic mass transport

A binary system in which the diffusion flux has a nonvanishing relaxation time is considered. We study the spectra of fluctuations of the solute density and the solute diffusion flux. The role of the diffusion flux is analyzed in two descriptions. First, the shortest observable time interval is shorter than the flux relaxation time, and the diffusion flux behaves as fluctuating independent variable. Second, the shortest observable time interval is longer than the flux relaxation time, and the diffusion flux behaves as a Markovian hydrodynamic noise.