Hydrodynamical field fluctuations in a non-equilibrium quasi-stationary state due to a temperature gradient

We consider a system in a state of non-equilibrium due to the introduction of a temperature gradient. The essential problem of this paper is to determine, in their most general form, the fluctuation correlation functions for hydrodynamical fields. We use a notation which enables us to distinguish the contributions from the individual mechanisms: contributions from fluctuations in number density, momentum and energy; contributions appearing due to having taken into account fluctuations in sound velocity and the heat conductivity coefficient; and ones related with the presence of the temperature gradient.