An important issue here. In 2001 Bojowald discovered that quantizing the basic (Friedmann) model of cosmology got rid of the classical singularity and typically replaced it by a bounce. A prior contracting phase leads up to the start of expansion.(adsbygoogle = window.adsbygoogle || []).push({});

In the years that followed Penrose raised the question of how one can reconcile the bounce cosmology with the Second Law. The entropy approaching crunch is very large and suddenly, after the bounce, the entropy of the born-again spacetime is very low. somehow it appears to be reset to zero. Penrose obviously found the bounce cosmology picture extremely interesting except for what he considered to be this terrible flaw---violating Thermodynamics. Since 2005 several of his lectures have focused on this issue.

What Bojowald and Tavakol have done is very creative. They seem to have found a way around Penrose objection to the bounce.

In doing so they have found a way of definingquantum entropy

http://arxiv.org/abs/0803.4484

Recollapsing quantum cosmologies and the question of entropy

Martin Bojowald, Reza Tavakol

23 pages, 2 figures

(Submitted on 31 Mar 2008)

"Recollapsing homogeneous and isotropic models present one of the key ingredients for cyclic scenarios. This is considered here within a quantum cosmological framework in presence of a free scalar field with, in turn, a negative cosmological constant and spatial curvature. Effective equations shed light on the quantum dynamics around a recollapsing phase and the evolution of state parameters such as fluctuations and correlations through such a turn around. In the models considered here, the squeezing of an initial state is found to be strictly monotonic in time during the expansion, turn around and contraction phases. The presence of such monotonicity is of potential importance in relation to a long standing intensive debate concerning the (a)symmetry between the expanding and contracting phases in a recollapsing universe. Furthermore, together with recent analogous results concerning a bounce one can extend this monotonicity throughout an entire cycle.This provides a strong motivation for employing the degree of squeezing as an alternative measure of (quantum) entropy. It may also serve as a new concept of emergent time described by a variable without classical analog.The evolution of the squeezing in emergent oscillating scenarios can in principle provide constraints on the viability of such models."

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# Quantum Entropy version of Second Law (Bojowald Tavakol)

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