  We analyze the diffusion of a Brownian particle in a fluid under stationary
flow. By using the scheme of non-equilibrium thermodynamics in phase space, we
obtain the Fokker-Planck equation which is compared with others derived from
kinetic theory and projector operator techniques. That equation exhibits
violation of the fluctuation dissipation-theorem. By implementing the
hydrodynamic regime described by the first moments of the non-equilibrium
distribution, we find relaxation equations for the diffusion current and
pressure tensor, allowing us to arrive at a complete description of the system
in the inertial and diffusion regimes. The simplicity and generality of the
method we propose, makes it applicable to more complex situations, often
encountered in problems of soft condensed matter, in which not only one but
more degrees of freedom are coupled to a non-equilibrium bath.
