I believe it is, but the answer is certainly model-dependent: it depends on your definition of 'cyclic' and 'entropy.'. Go to arXiv, a search for papers containing those two words in the abstract gave 36 answers for the years 2006-2013.

Wikipedia:

‘’The conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity, advanced by the theoretical physicists Roger Penrose and Vahe Gurzadyan. [1][2] In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big Bang singularity of the next.’’

http://www.physicsforums.com/showthread.php?t=672004

‘’In that model, the big bang was a state of tiny entropy because if we accept the law of 'ever increasing entropy', i.e. 2nd law of thermodynamics (which Penrose explains in every detail), then going backwards in time mist take us to states of ever decreasing entropy. Going way back to the big bang, we see it must have a very low entropy.’’

Louis

I think the texts you quote do not address the question. Surely, in a universe starting from a big bang the entropy has increased from nothing or from a very small value.

But the question at hand, rephrased, is: what happens to that enormous amount of accumulated entropy if the universe collapses to a point? The 2nd law does not permit its destruction, so the burden of invention is on the people constructing cycling models.I have only seen some hand-waving arguments.

Incidentally, even the best experts on black holes do not understand what happens to the entropy of in-falling matter.

Matt,

In Penrose`s cyclic model, there is no distinction between a verry small region of space and an infinite uniform region. There is no collapse but an infinite expansion in that model. Entropy is a notion that require two levels: a macroscopic level and a microscopic level. If only one level exist then the whole concept dissappear.

I’ve recently proposed a new type of cyclic model containing an asymptotically flat gravitational potential and embedded bulk flows. Entropy in this perspective is constant globally and therefore does not violate the laws of thermodynamics. The entire theory including predictions and proofs is available in my paper “The Theory of Everything” on researchgate (see pages 38 - 40, 42, 48 – 52 and 59 - 61). It was scheduled to be published in April, but the journal asked me to reduce the length by over 300% at the last minute; so I’m currently writing a shorter version. Here is a quick overview of how entropy works in this perspective.

1. The local space emerges from a dense relativistic jet, much larger than those observed locally. The product of this jet will of course have low metallicity and high temperature.

2. As the relativistic jet moves out of the asymptotically flat gravitational potential, it cools and expands. The jet further enters the local space in the form of the “dark flow”.

3. Our perspective from Earth consists of residual thermal expansion locally, while the inferred accelerated expansion occurs due to the deflection of geodesics towards the center of an asymptotically flat gravitational potential.

4. Relatively older galaxies and clusters begin to accelerate into this potential with increased metallicity and cold baryonic matter. For example, high redshift clusters consist of reionized hydrogen (lyman-alpha blobs) rather than hot, x-ray emitting gas. Galaxies are also observed to have increasing cold baryonic matter with redshift.

5. Momentum is conserved by a central core, where the inflow of galaxies and clusters produces two relativistic jets. The cosmic background radiation also originates from the surface of the central core in the form of black body radiation.

This of course isn't a cyclic model in the usual sense, as these bulk flows are continuous (a steady state). An observer within the flow however will see the universe as cyclical.

Michael,

Maybe your full paper was clearer. Here you have reduced it beyond comprehensibility.