Boltzmann entropy of a Newtonian Universe

Abstract

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.

arXiv comment15 pages

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Cited by in corpus (5)

• $L^p$-Spectrum of the Schrödinger Operator with Inverted Harmonic Oscillator Potential
• The cosmological constant of emergent spacetime in the Newtonian approximation
• On the holographic bound in Newtonian cosmology
• Spherical space in the Newtonian limit: The cosmological constant
• Hyperbolic space in the Newtonian limit: the cosmological constant