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Entropy 2016, 18(1), 34;

Schroedinger vs. Navier–Stokes

Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Valencia 46022, Spain
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editor: Ronnie Kosloff
Received: 17 November 2015 / Accepted: 13 January 2016 / Published: 19 January 2016
(This article belongs to the Special Issue Quantum Thermodynamics)
View Full-Text   |   Download PDF [241 KB, uploaded 19 January 2016]


Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck’s constant, while the volume density of entropy is proportional to Boltzmann’s constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier–Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation). View Full-Text
Keywords: quantum mechanics; irreversible thermodynamics quantum mechanics; irreversible thermodynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Fernández de Córdoba, P.; Isidro, J.M.; Vázquez Molina, J. Schroedinger vs. Navier–Stokes. Entropy 2016, 18, 34.

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