Schroedinger vs. Navier–Stokes

Córdoba, Pedro Fernández de; Isidro, J. M.; Molina, J. Vazquez

doi:10.3390/e18010034

Cited by 9 publications

(6 citation statements)

References 45 publications

(79 reference statements)

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“…As a consistency check we observe that, in the limit τ 2 → ∞, the conditional probability (13) reduces to the unconditional probability (8). Using the Chapman-Kolmogorov equation (11) one can reexpress the conditional probability (13) as…”

Section: Basics In Irreversible Thermodynamicsmentioning

confidence: 86%

“…Equipped with thermodynamical tools as befits any emergent theory, we have in refs. [11,12,13] developed a framework that maps semiclassical quantum mechanics onto the classical thermodynamics of irreversible processes in the linear regime, the latter as developed by Onsager, Prigogine and collaborators [23,27]. Within this framework, the statement often found in the literature, quantisation is dissipation [4], can be given a new interpretation.…”

Section: Introductionmentioning

confidence: 99%

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The Holographic Quantum

2016

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Section: Basics In Irreversible Thermodynamicsmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

The Holographic Quantum

2016

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“…The notion that quantum mechanics is an emergent theory has been discussed at length in the literature [1][2][3][4][5][6][7]. Combined with the idea that spacetime is also is an emergent phenomenon [8][9][10][11][12], this paves the way for a computation of some thermodynamical properties of spacetime in quantum-mechanical terms.…”

Section: The Approach Via Emergent Quantum Theorymentioning

confidence: 99%

Boltzmann Entropy of a Newtonian Universe

Cabrera

Córdoba

Isidro

2017

Entropy

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A dynamical estimate is given for the Boltzmann entropy of the Universe, under the simplifying assumptions provided by Newtonian cosmology. We first model the cosmological fluid as the probability fluid of a quantum-mechanical system. Next, following current ideas about the emergence of spacetime, we regard gravitational equipotentials as isoentropic surfaces. Therefore, gravitational entropy is proportional to the vacuum expectation value of the gravitational potential in a certain quantum state describing the matter contents of the Universe. The entropy of the matter sector can also be computed. While providing values of the entropy that turn out to be somewhat higher than existing estimates, our results are in perfect compliance with the upper bound set by the holographic principle.Keywords: newtonian cosmology; emergent quantum theory The Approach via Emergent Quantum TheoryIn this article, we will argue in favour of emergent quantum mechanics as providing an appropriate framework to estimate thermodynamical quantities of the Universe, such as the entropy.The notion that quantum mechanics is an emergent theory has been discussed at length in the literature [1][2][3][4][5][6][7]. Combined with the idea that spacetime is also is an emergent phenomenon [8][9][10][11][12], this paves the way for a computation of some thermodynamical properties of spacetime in quantum-mechanical terms. We would like to remark that a quantum-mechanical approach to the expansion of the Universe was called for long ago in Reference [13], where it was suggested to regard the expansion of the Universe as a scattering problem in quantum mechanics.The expansion of the Universe is a long-standing experimental observation [14] that has in recent years been refined thanks to very precise measurements [15,16]. In the Newtonian approximation, this receding behaviour of the galaxies can be easily modelled by a phenomenological potential-namely, an isotropic harmonic potential carrying a negative sign:As the angular frequency, we take the current value of Hubble's constant H 0 . Thus, U Hubble has the dimensions of energy per unit mass, or velocity squared.In the emergent approach to spacetime presented in Reference [12], gravity qualifies as an entropic force. If gravitational forces are entropy gradients, gravitational equipotential surfaces can be identified with isoentropic surfaces. Recalling the arguments of Reference [12], a classical point particle approaching a holographic screen causes the entropy of the latter to increase by one quantum k B . Here we will analyse a quantum-mechanical model in which the forces driving the galaxies away from each other can be modelled by the Hubble potential (1). We will replace the classical particle of Reference [12] with a collection of quantum particles (the matter contents of the Universe) described

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“…Invoking the correspondence principle, this factorisation expresses the phase of ψ as the (complex) exponential of the classical action I. For the amplitude of ψ one invokes Boltzmann's principle and Born's rule in order to write it as the (real) exponential of the entropy S [3]. Altogether one writes the wavefunction as…”

Section: Introductionmentioning

confidence: 99%

“…Using the decompostion (3), in ref. [3] we have analysed the properties of nonstationary quantum states. In the present letter we will analyse stationary states instead.…”

Section: Introductionmentioning

confidence: 99%

Amplitude, phase, and complex analyticity

Cabrera,

de Cordoba,

Isidro

2017

Preprint

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Expressing the Schroedinger Lagrangian L in terms of the quantum wavefunction ψ = exp(S + iI) yields the conserved Noether current J = exp(2S)∇I. When ψ is a stationary state, the divergence of J vanishes. One can exchange S with I to obtain a new Lagrangian L and a new Noether current J = exp(2I)∇S, conserved under the equations of motion of L. However this new current J is generally not conserved under the equations of motion of the original Lagrangian L. We analyse the role played by J in the case when classical configuration space is a complex manifold, and relate its nonvanishing divergence to the inexistence of complex-analytic wavefunctions in the quantum theory described by L.

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Schroedinger vs. Navier–Stokes

Cited by 9 publications

References 45 publications

The Holographic Quantum

The Holographic Quantum

Boltzmann Entropy of a Newtonian Universe

Amplitude, phase, and complex analyticity

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