Maximum Entropy Reachable Before the Next Turnaround in a Recollapsing Branch

The reachable entropy falls far short of the maximum. A recollapsing branch turns around while still, thermodynamically, in its youth: heat death in the strict sense of saturating the bound is not achieved even given the full expansion lifetime, because the production rate is too slow compared with the size of the bound. The computation is performed from stated assumptions in a density-limited bounce, in which the neutron-branch limit density sets a maximum density, a finite bounce temperature, and a minimum horizon size. Headline values from the deposited calculation are: S_max_kB = 2.90e+122; t_turnaround_s = 1.58e+18; t_turnaround_yr = 5.00e+10; S_gain_by_turnaround_kB = 3.47e+104; S_at_turnaround_kB = 4.47e+104; fraction_of_max = 1.54e-18. The study is simulated and computed, not measured, and its conclusions are stated at the precision the stated assumptions support.