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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”.