  Penrose [1] has emphasized how the initial big bang singularity requires a
special low entropy state. We address how recent brane cosmological schemes
address this problem and whether they offer any apparent resolution. Pushing
the start time back to $t=-\infty$ or utilizing maximally symmetric AdS spaces
simply exacerbates or transfers the problem.
  Because the entropy of de Sitter space is $S\leq 1/\Lambda$, using the
present acceleration of the universe as a low energy $(\Lambda\sim 10^{-120}$)
inflationary stage, as in cyclic ekpyrotic models, produces a gravitational
heat death after one cycle. Only higher energy driven inflation, together with
a suitable, quantum gravity holography style, restriction on {\em ab initio}
degrees of freedom, gives a suitable low entropy initial state. We question the
suggestion that a high energy inflationary stage could be naturally reentered
by Poincare recurrence within a finite causal region of an accelerating
universe.
  We further give a heuristic argument that so-called eternal inflation is not
consistent with the 2nd law of thermodynamics within a causal patch.
