Schroedinger vs. Navier–Stokes
AbstractQuantum 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
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Fernández de Córdoba, P.; Isidro, J.M.; Vázquez Molina, J. Schroedinger vs. Navier–Stokes. Entropy 2016, 18, 34.
Fernández de Córdoba P, Isidro JM, Vázquez Molina J. Schroedinger vs. Navier–Stokes. Entropy. 2016; 18(1):34.Chicago/Turabian Style
Fernández de Córdoba, P.; Isidro, J. M.; Vázquez Molina, J. 2016. "Schroedinger vs. Navier–Stokes." Entropy 18, no. 1: 34.
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