Abstract
It is shown on the basis of hydrodynamic fluctuation theory that the generalized fluctuation-dissipation theorem derived for brownian motion in incompressible liquids is also valid for the case of compressible fluids. The equations used to demonstrate this are the linearized hydrodynamic equations for compressible liquids. The resistance factor for time-dependent motion of a spherical particle is derived, and it is shown that the autocorrelation functions for random force and velocity change with degree of compressibility in a continuous fashion. The asymptotic behavior of these correlation functions for large times is not affected by the compressibility.
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