On Connections between the Quantum and Hydrodynamical Pictures of Matter

TL;DR

This paper develops a model-independent quantum statistical framework connecting quantum microdynamics with classical hydrodynamics, emphasizing large-scale conserved observables and extending Onsager relations to nonequilibrium steady states.

Contribution

It introduces a general, model-independent approach linking quantum and hydrodynamical descriptions, extending Onsager's relations and fluctuation theory to nonequilibrium steady states.

Findings

Establishes generalized Onsager reciprocity relations for nonequilibrium states.

Shows that hydrodynamical fluctuations exhibit long-range spatial correlations.

Provides a bridge between quantum microdynamics and classical continuum mechanics.

Abstract

We present a general, model-independent, quantum statistical treatment of the connection between the quantum and hydrodynamical pictures of reservoir driven macroscopic systems. This treatment is centred on the large scale properties of locally conserved hydrodynamical observables and is designed to form a bridge between quantum microdynamics and classical macroscopic continuum mechanics, rather than a derivation of the latter from the former. The key assumptions on which the treatment is based are hypotheses of chaoticity and local equilibrium for the hydrodynamical fluctuations around nonequilibrium steady states, together with an extension of Onsager's regrssion hypothesis to those states. On this basis, we establish canonical generalisations of both the Onsager reciprocity relations and the Onsager-Machlup fluctuation theory to nonequilibrium steady states, and we show that the spatial correlations of the hydrodynamical fluctuations are generically of long range in these states.