Macrostatistics and Fluctuating Hydrodynamics

TL;DR

This paper extends macrostatistical methods to viscous fluids, demonstrating that hydrodynamical fluctuations in nonequilibrium steady states follow a Gaussian Markov process with long-range correlations, based on finite system models.

Contribution

It introduces a finite-system macrostatistical framework for viscous fluids, generalizing Landau's fluctuating hydrodynamics to nonequilibrium steady states.

Findings

Hydrodynamical fluctuations follow a Gaussian Markov process.

Fluctuations exhibit long-range spatial correlations.

Framework applies to finite, viscous fluid systems.

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.