Isn’t all this just punning on definitions? If the particle velocities in a gas are Maxwell-Boltzmann distributed for some parameter T, we can say that the gas has “Maxwell-Boltzmann temperature T”. Then there is a separate Jaynes-style definition about “temperature” in terms of the knowledge someone has about the gas. If all you know is that the velocities follow a certain distribution, then the two definitions coincide. But if you happen to know more about it, it is still the case that almost all interesting properties follow from the coarse-grained velocity distribution (the gas will still melt icecubes and so on), so rather than saying that it has zero temperature, should we not just note that the information-based definition no longer captures the ordinary notion of temperate?
Isn’t all this just punning on definitions? If the particle velocities in a gas are Maxwell-Boltzmann distributed for some parameter T, we can say that the gas has “Maxwell-Boltzmann temperature T”. Then there is a separate Jaynes-style definition about “temperature” in terms of the knowledge someone has about the gas. If all you know is that the velocities follow a certain distribution, then the two definitions coincide. But if you happen to know more about it, it is still the case that almost all interesting properties follow from the coarse-grained velocity distribution (the gas will still melt icecubes and so on), so rather than saying that it has zero temperature, should we not just note that the information-based definition no longer captures the ordinary notion of temperate?