  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.
