[nwallin]

> If there is no system of parts, there is no entropy.

Define entropy?

Wikipedia says this about entropy:

> In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Entropy expresses the number Ω of different configurations that a system defined by macroscopic variables could assume.

The number of possible configurations of a black hole is hilariously large and demands delving into up arrows and beyond. It includes collapsing stellar cores, primordial black holes, neutron stars accreting matter until collapse, merging black holes, kugelblitzes, etc., which all are bizarrely dislike microstatically. Yet the possible macroscopic variables are only three: Mass, angular momentum, and charge.

If you pretend quantum mechanics don't exist, sure, black holes don't have entropy. But we're pretty sure something that looks a lot like quantum mechanics does exist.

[ziotom78]

Moreover, entropy can be defined using either thermodynamics or statistical mechanics. In the first case (which was the first to be developed, historically) the entropy exists for any isolated system in thermal equilibrium, even though the system can be subdivided into parts or not.