It is speculated how dark energy in a braneworld can help reconcile an infinitely cyclic cosmology with the second law of thermodynamics. A cyclic model featuring dark energy with a phantom (w<-1) equation of state leads to a turnaround at a time just before a would-be Big Rip at one end of the cycle and a bounce just before a would be crunch at the other. At the turnaround, both the volume and entropy of our universe decrease by a gigantic factor while very many independent small contracting universes are spawned. The entropy of our model decreases to nearly zero as it approaches the turnaround after which it increases by only a vanishing amount during the contracting stage, empty of matter. Shortly after the bounce, the entropy increases by a large factor during inflationary expansion. We next examine the content of the contracting universe (cu) and its entropy Scu. We find that in addition to dark energy, the universe contains zero photons on average (with the unlikely single photon, if present immediately after the turnaround, having infinitesimal energy that blue shifts eventually to produce e+e- pairs). These statements are independent of the equation of state ω = p / ρ of dark energy provided omega < -1. Thus Scu = 0 and if observations confirm omega < -1 the entropy problem is solved. We discuss the absence of a theoretical lower bound on phi = |omega; + 1 | and then describe an anthropic fine tuning argument that renders unlikely an extremely small phi. The present bound phi < 0.1 already implies a time until turnaround of (tT - t0) > 100 Gy. The requirement that our universe satisfy a CBE-condition (Comes Back Empty) imposes a lower bound on the number Ncp of causal patches which separate at turnaround. This bound depends on the dark energy equation of state w = p \ rho = -1 - phi with phi > 0. More accurate measurement of phi will constrain Ncp. The critical density rhoc in the model has a lower bound rhoc is greater than or equal to ge (109 GeV)4 or rhoc is greater than or equal to ge (1018 GeV)4 when the smallest bound state has size 10-15m, or 10-35m, respectively.