[derbOac]

I've read and watched different attempts at explaining negative temperature, and the Wikipedia article is actually the one that has made the most sense to me.

The concept still seems "off" to me intuitively, like an abuse of notation or something, although I understand it logically.

[Anon84]

It's usually a consequence of working in the microcanonical ensemble, where you're forcing the energy of the system to be fixed while exploring its various states. The most common (and intuitive) scenario is the Macrocanonical ensemble where the temperature is fixed the energy is allowed to vary. In this case, of course, there is no negative temperature.