The paper discusses recent proposals by Carroll and Chen, as well as Barbour,
Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a
Past Hypothesis, i.e., the assumption of a special (low-entropy) initial state
of the universe. After discussing the role of the Past Hypothesis and the
controversy about its status, we explain why Carroll's model - which
establishes an arrow of time as typical - can ground sensible predictions and
retrodictions without assuming something akin to a Past Hypothesis. We then
propose a definition of a Boltzmann entropy for a classical N-particle system
with gravity, suggesting that a Newtonian gravitating universe might provide a
relevant example of Carroll's entropy model. This invites comparison with the
work of Barbour, Koslowski, and Mercati that identifies typical arrows of time
in a relational formulation of classical gravity on shape space. We clarify the
difference between this gravitational arrow in terms of shape complexity and
the entropic arrow in absolute spacetime and work out the key advantages of the
relationalist theory. We end by pointing out why the entropy concept relies on
absolute scales and is thus not relational.Comment: Contains small corrections with respect to the previous versio