Macrostatistics and Fluctuating Hydrodynamics

Abstract

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 be based on the generic model of a large but finite system, rather than an infinite one. On this basis, together with assumptions of Onsager's 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 Landau's fluctuating hydrodynamics and generically carries long range spatial correlations.

Revised article, with some minor corrections. To be published in "Reports on Mathematical Physics"

References in corpus (4)

• Macroscopic fluctuation theory for stationary non equilibrium states
• Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process
• On the Question of Temperature Transformations under Lorentz and Galilei Boosts
• Quantum macrostatistical picture of nonequilibrium steady states

Cited by in corpus (1)

• Local Thermodynamic Equilibrium at Three Levels