On the physical origin of long-ranged fluctuations in fluids in thermal nonequilibrium states

Thermodynamic fluctuations in systems that are in nonequilibrium steady states are always spatially long ranged, in contrast to fluctuations in thermodynamic equilibrium. In the present paper we consider a fluid subjected to a stationary temperature gradient. Two different physical mechanisms have been identified by which the temperature gradient causes long-ranged fluctuations. One cause is the presence of couplings between fluctuating fields. Secondly, spatial variation of the strength of random forces, resulting from the local version of the fluctua-tion-dissipation theorem, has also been shown to generate long-ranged fluctua-tions. We evaluate the contributions to the long-ranged temperature fluctuations due to both mechanisms. While the inhomogeneously correlated Langevin noise does lead to long-ranged fluctuations, in practice, they turn out to be negligible as compared to nonequilibrium temperature fluctuations resulting from the coupling between temperature and velocity fluctuations. KEY WORDS: Fluctuating hydrodynamics; long-ranged correlations; nonequi-librium fluctuations; nonequilibrium steady states; temperature fluctuations