Here’s the misunderstanding. Your example above, where all spins are in their highest possible energy state, really has temperature T=-0, an infinitesimal temp

Here’s the misunderstanding. Your example above, where all spins are in their highest possible energy state, really has temperature T=-0, an infinitesimal temperature just below absolute zero. This would not be the negative temperature possible. You are correct that energy would flow out of this maximal-energy system. But it corresponds to System B in my example - the system at the less negative temperature. The animation near the top of the article shows this nicely. The particles approach their max possible state as T flips to negative and approaches zero from below. Temperatures of positive and negative infinity are statistically equivalent in this example, where states of any energy are equally likely. It’s only at smaller less-negative temperatures where the population inversion occurs.