  A generalization of the random fluid hydrodynamic fluctuation theory due to
Landau and Lifshitz is applied to describe cosmological fluctuations in systems
with radiation and scalar fields. The viscous pressures, parametrized in terms
of the bulk and shear viscosity coefficients, and the respective random
fluctuations in the radiation fluid are combined with the stochastic and
dissipative scalar evolution equation. This results in a complete set of
equations describing the perturbations in both scalar and radiation fluids.
These derived equations are then studied, as an example, in the context of warm
inflation. Similar treatments can be done for other cosmological early universe
scenarios involving thermal or statistical fluctuations.
