Negative absolute temperature is a thing. Lasers exhibit negative temperatures when active, i.e. the lasing medium has a negative temperature expressed in Kelvin. Adding more energy doesn't increase its entropy, it just turns into more laser light. Any such system with bounded entropy can have a negative thermodynamic temperature.

[–] Zaphod@discuss.tchncs.de 2 points 11 months ago

I had a suspicion there was going to be a response like this. Never heard of it but sounds very interesting.
I doubt I'll properly understand it without a good YouTube video. I shall embark on a search