ΔE=kT log(2) ⇒ N₂/N₁ = 1/2, log ratio = -log(2) (one-bit population split)

Sympy-exact symbolic witness of the one-bit (factor-of-2) population split between two quantum levels at the log-unit Boltzmann-factor threshold. Setup: pick ΔE = kT · log(2) so ΔE/(kT) = log(2) ⇒ N₂/N₁ = exp(−log(2)) = 1/2 exactly. …