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negative temperatures bay bee
Negative temperature means that the system loses entropy if you put more energy in. This means that negative temp is hotter than any positive temperature, in the sense that if you put two systems in thermal contact, heat will flow from negative to positive.
In the continuum of temperatures, positive absolute zero is the coldest, going up to positive infinity Kelvins. Then minus infinity Kelvins is just slightly hotter than positive infinity. Then it keeps going up to negative absolute zero, the hottest temperature.
These infinities keep cropping up because the reciprocal of temperature is actually the more fundamental physical quantity.
Negative temperature means that the system loses entropy if you put more energy in.
Of course that's basically the same as the "you travel backwards in time if you move faster than light" in the sense that these are things the math does, if you put in these totally unphysical values, while the same set of rules that give this predictions say you can't reach these values.
Not really, as negative temperature has been experimentally measured.
Ah, yes. You're referring to these gases with an inverted energy distribution. I guess that's a question of definition, since they don't exist in the thermodynamic limit.
These infinities keep cropping up because the reciprocal of temperature is actually the more fundamental physical quantity.
I'm interested in reading more about this. I'm looking at the Wikipedia page for "Thermodynamic beta" now. Is that what you're talking about?
Yes that's it. Fun fact: The entropy is basically the most fundamental thermodynamical quantity, but was discoverd long after temperature and energy. If that would not be the case, we might measure temperature in eV / kByte, since the unit of temperature is energy / entropy and the unit of entropy is information.
In a sense, the existence of the Boltzmann constant is a historical accident, because temperature and energy have been discovered after entropy.
Also look at "Negative Temperature".
Mmm... gotta love below 0 Kelvin.