Coarse-Graining and the Second Law in the Contracting Branch of a Bounce

Clumping produces coarse-grained entropy in contraction at a scale that is a substantial fraction of the present radiation entropy, and nothing in the estimate changes sign when the expansion reverses. Contraction is not a rewind: structures that form while the universe contracts dissipate and virialise in the ordinary direction, generating entropy as they do so. 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: dS_clumping_kB = 8.26e+79; tff_now_s = 7.00e+17; tff_1000x_s = 2.21e+16; fraction_of_present_entropy = 2.75e-10. The study is simulated and computed, not measured, and its conclusions are stated at the precision the stated assumptions support.