Fluctuation‐dissipation theorems on the basis of hydrodynamic propagators

TLDR: In this paper, the velocity correlation functions describe a source with time-dependent or independent Oseen propagators, and 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.

Abstract: 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 th...