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.)
(Disclaimer: very poor knowledge of physics here, just interpreting the article)
http://www.physorg.com/print209708826.html
- looks like there are many of them, as non-creationists would expect
The really good news is
> In the past, Penrose has investigated cyclic cosmology models because he has noticed another shortcoming of the much more widely accepted inflationary theory: it cannot explain why there was such low entropy at the beginning of the universe. The low entropy state (or high degree of order) was essential for making complex matter possible.
Which I interpret to mean information passes through the Big Crunch/Big Bang cycle. No heat death, information passes through - good news for transhumanists?