Fluctuating hydrodynamics for a rarefied gas based on extended thermodynamics

We develop a theory of fluctuating hydrodynamics based on extended thermodynamics through studying the 13-variable theory for a monatomic rarefied gas as a representative case. After analyzing the relationship between the present theory and the Landau-Lifshitz theory, we discuss the hierarchy structure of the hydrodynamic fluctuations. -- Highlights: → We develop a theory of fluctuating hydrodynamics based on extended thermodynamics. → We make clear the relationship between the present theory and the Landau-Lifshitz theory. → We find the general hierarchy structure of the hydrodynamic fluctuations basing on extended thermodynamics.