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Schroedinger vs. Navier–Stokes

Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Valencia 46022, Spain
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Ronnie Kosloff
Entropy 2016, 18(1), 34; https://doi.org/10.3390/e18010034
Received: 17 November 2015 / Accepted: 13 January 2016 / Published: 19 January 2016
(This article belongs to the Special Issue Quantum Thermodynamics)
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
MDPI and ACS Style

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

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