  It is suggested that dark energy in a brane world can help reconcile an
infinitely cyclic cosmology with the second law of thermodynamics. A cyclic
cosmology is described, in which dark energy with constant equation of state
leads to a turnaround at finite future time, when entropy is decreased by a
huge factor equal to the inverse of its enhancement during the initial
inflation. Thermodynamic consistency of cyclicity requires the arrow of time to
reverse during contraction. Entropy reduction in the contracting phase is
infinitesimally smaller than entropy increase during expansion.
