[Y_Y]

Negative temperature is a perfectly normal and well-studied phenomenon with lots of common examples. Temperature is defined as the rate of change of entropy wrt internal energy, usually more energy means more entropy, but it's not a given.

https://en.wikipedia.org/wiki/Negative_temperature

[aziaziazi]

> A system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system

Wait what?!! That feeds my daily “oh oooh” moment.

[Y_Y]

Energy flow wants to maximize entropy. Usually things flow from hot to cold because a cold thing will "make better use" of the energy to create entropy (i.e. permit microstates). Something with negative temperature will increase entropy by losing energy, and the positive temperature thing will increase entropy by gaining it, so it's (thermodynamically) a no-brainer.

[eru]

It makes more sense, if you don't measure in temperature, but in 'coldness'. See https://en.wikipedia.org/wiki/Coldness or β.

Basically, coldness is 1/temperature but makes more theoretical sense:

> Though completely equivalent in conceptual content to temperature, β is generally considered a more fundamental quantity than temperature owing to the phenomenon of negative temperature, in which β is continuous as it crosses zero whereas T has a singularity.[6]

> In addition, β has the advantage of being easier to understand causally: If a small amount of heat is added to a system, β is the increase in entropy divided by the increase in heat. Temperature is difficult to interpret in the same sense, as it is not possible to "Add entropy" to a system except indirectly, by modifying other quantities such as temperature, volume, or number of particles.