Brownian motion in a fluid near its critical point II: The fluctuation-dissipation theorem

Fluctuation-dissipation theorems for the random force and the random torque on a Brownian particle of arbitrary shape immersed in a fluid close to its critical point are derived from fluctuating hydrodynamics, taking also into account the temperature fluctuations in the fluid. It is assumed that the particle is either a perfect insulator for heat or an ideal conductor. In the latter case the fluctuation-dissipation theorems involve also the random heat source generated by the fluid fluctuations.