Boltzmann entropy of a Newtonian Universe

TL;DR

This paper estimates the Boltzmann entropy of the Universe using Newtonian cosmology, modeling the cosmic fluid quantum-mechanically and relating gravitational entropy to the vacuum expectation of the gravitational potential.

Contribution

It introduces a novel quantum-mechanical approach to estimate cosmic entropy and links gravitational entropy to quantum vacuum expectations within Newtonian cosmology.

Findings

Entropy estimates are higher than previous calculations.

Results comply with the holographic principle's upper bound.

Provides a new framework connecting quantum mechanics and cosmological entropy.

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.