Explaining classical black hole thermodynamics from type-II entropy and relative state-counting

Determine whether the type II von Neumann algebra framework for renormalized entropy differences and the associated relative state-counting of semiclassical black holes can be used to derive or explain the classical laws of black hole thermodynamics, in an analogous manner to how Boltzmann–Gibbs statistical mechanics explains the laws of thermodynamics for ordinary matter.

Background

Recent work identifies a type II algebra of physical observables in semiclassical black hole settings, enabling well-defined renormalized entropy differences and a notion of relative state-counting. These constructions are consistent with the Bekenstein–Hawking entropy when regulated appropriately and support a statistical-mechanical interpretation of semiclassical black hole entropy.

It remains to be understood whether this algebraic and information-theoretic framework can reproduce the classical laws of black hole mechanics in a manner fully analogous to the Boltzmann–Gibbs account of thermodynamics for ordinary matter systems.