As I understand it, Penrose's CCC posits that the universe will become "space-like" in the far future because all matter will be absorbed by black holes and eventually re-emitted as photons; thus it will be impossible even in theory to build any kind of clock after this occurs. (This also means total information entropy.)

(This summary comes from my probably flawed understanding of Penrose's description of CCC in the book On Space and Time.)