Macrostatistics and Fluctuating Hydrodynamics

We extend our earlier macrostatistical treatment of hydrodynamical fluctuations about nonequilibrium steady states to viscous fluids. Since the scale dependence of the Navier–Stokes equations precludes the applicability of any infinite scale (hydrodynamical) limit, this has to based on the generic model of a large but finite system, rather than an infinite one. On this basis, together with the assumption of Onsagerʹs regression hypothesis and conditions of local equilibrium and chaoticity, we show that the hydrodynamical fluctuations of a reservoir driven fluid about a nonequilibrium steady state execute a Gaussian Markov process that constitutes a mathematical structure for a generalised version of Landauʹs fluctuating hydrodynamics and generically carries long range spatial correlations.