We present a thermodynamic and stochastic theory of coupled transport processes, thermal conduction, and viscous flow and apply this development to Rayleigh scattering experiments in simple fluids removed from equilibrium by the imposition of a temperature gradient. In the linearized region ground the conductive steady state, the inhomogeneous fluctuations obey a linear Fokker-Planck equation, equivalent to the equations of fluctuating hydrodynamics. The stationary probability distribution, from which the density-density correlations measured in the scattering experiments can be derived, is expressed in terms of the action of the Fokker-Planck Lagrangian along the most probable path for the generation of a particular fluctuation away from the steady state. This action is proportional to a defined deterministic excess work, which is evaluated by integrating along the deterministic trajectory the difference between the maximum work available in an infinitesimal change of the random variables and the same quantity when this change occurs in a reference state. Thus we provide a thermodynamic theory complementary to fluctuating hydrodynamics in terms of this excess work.