On Connections between the Quantum and Hydrodynamical Pictures of Matter

Details On Connections between the Quantum and Hydrodynamical Pictures of Matter On Connections between the Quantum and Hydrodynamical Pictures of Matter

2007-10-05

arxiv.org/abs/0710.1239v1

Physics

Mathematical Physics

To be published in "Modern Encyclopedia of Mathematical Physics"

Scientific paper

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.

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