[cbolton]

I find your explanation much better than the one at https://simple.wikipedia.org/wiki/Negative_temperature, please consider expanding that page a bit!

Back to the substance of the topic: I feel let down here, negative temperature sounds like something amazing but it turns out to be more of a quirk due to the definition. I wonder if physicists would have chosen this definition, if had they been aware of this when they did.

Also I wonder if there's an intensive thermodynamic property that actually says how much thermal energy is in the system, since temperature apparently won't do it?

[Rayhem]

> Also I wonder if there's an intensive thermodynamic property that actually says how much thermal energy is in the system, since temperature apparently won't do it?

Thermodynamic beta[1] does exactly that. If we consider temperature as "tendency to give energy away", then the scale starts at zero, heads out through positive infinity, comes in through negative infinity, and then stops at negative zero. I.e. if T_a > T_b > 0, then system a gives energy to system b. Then, if T_c < T_d < 0, then system d gives energy to system c.

Thermodynamic beta (really just 1/T, the "coldness" of a system) fixes this: if B_a < B_b anywhere on the number line, then B_b is colder than B_a.

[1]: https://en.wikipedia.org/wiki/Thermodynamic_beta