Not yet reviewed by Pith; the record is open.

We explore how the assumption of ionization equilibrium modulates the modeled intergalactic medium (IGM) at the end of the hydrogen Epoch of Reionization using the cosmological radiation hydrodynamic \textsc{Technicolor Dawn} simulation. In neutral and partially-ionized regions where the metagalactic ultraviolet background (UVB) is weak, the ionization timescale $t_\mathrm{ion}\equiv \Gamma^{-1}$ exceeds the Hubble time. Assuming photoionization equilibrium in such regions artificially boosts the ionization rate, accelerating reionization. By contrast, the recombination time $t_\mathrm{rec} < t_\mathrm{ion}$ in photoionized regions, with the result that assuming photoionization equilibrium artificially increases the neutral hydrogen fraction. Using snapshots between $8 \geq z \geq 5$, we compare the predicted Lyman-$\alpha$ forest flux power spectrum with and without the assumption of ionization equilibrium. Small scales ($k > 0.1$ rad s km$^{-1}$) exhibit reduced power from $7 \leq z \leq 5.5$ in the ionization equilibrium case while larger scales are unaffected. This occurs for the same reasons: ionization equilibrium artificially suppresses the neutral fraction in self-shielded gas and boosts ionizations in voids, suppressing small-scale fluctuations in the ionization field. When the volume-averaged neutral fraction drops below $10^{-4}$, the signature of non-equilibrium ionizations on the Lyman-$\alpha$ forest (LAF) disappears. Comparing with recent observations indicates that these non-equilibrium effects are not yet observable in the LAF flux power spectrum.