Entropy per Baryon Across a Torsion Bounce: The Size of the Adiabatic Violation in the Effective Description

The net fractional change in comoving entropy across the bounce is 0.0 at a peak density ratio of unity: in this effective description the entropy that leaves the bounce equals the entropy that entered, exactly, because the correction is a function of density alone and the trajectory retraces its densities. The transient deviation during the crossing is a different matter. At a peak ratio of 0.1 the comoving entropy computed from the effective density departs from its adiabatic value by at most 0.076; at a peak ratio of 0.5 the maximum departure is 0.405; and at a peak ratio of 1.0 it reaches 1.000. The entropy per baryon is therefore conserved across the event but not during it: midway through the bounce the effective bookkeeping assigns the radiation a substantially different entropy than the adiabatic value, and the assignment reverts as the density falls. The study is a computation from stated assumptions, performed by the accompanying script; it is simulated, not measured.