Fluctuation-dissipation theorems on the basis of hydrodynamic propagators

Hydrodynamic propagators of forces are formulated and studied in the following cases: for uniform temperature, neglecting convection or using Oseen's linearization, with or without compressibility, and also for nonuniform temperature. Discussions and comparisons are given wherever possible. Such a propagator formalism is useful in cases of hydrodynamic interactions among solid bodies, as well as thermodynamic fluctuation forces. It is found that the velocity correlation functions describe a source with time-dependent or -independent Oseen propagators. The correlation of pressure fluctuations, which exists even in the absence of dissipation, agrees with the result derived from the relaxation function of the mechanical fluctuation-dissipation theorem, as well as with the thermodynamic equilibrium correlation. The correlation of temperature fluctuations describes a diffusion process of the variance κ/ρ0cp when cp = cν. In accordance with Curie's principle of nonequilibrium thermodynamics, it is found that the transverse vector field is not coupled to the scalar fields. Finally, a possible comparison with a wind tunnel experiment on temperature fluctuations is indicated.