I know about Wick rotation, but I’m curious about the converse—have you ever heard of someone using imaginary temperature?
It’s not even all that crazy—the Boltzmann distribution would just be sinuosidal. A cursory googling also turns up the notion of expanding phase diagrams of simple lattice models to the complex temperature plane. But I’ve never heard of an actual case where this would show up (unlike negative temperature which has justifying examples like lasers).
Thank you! As a technique, there is so-called Matsubara frequency calculation using something like imaginary temperature (not exactly, but it is the closest thing I can think about).
From the physical point of view, the imaginary temperature would mean complex probabilities, which is a very strange thing. From a frequentist approach, they do not make sense at all. From bayesian approach, we potentially can define it, but still not clear what would they mean.
Fun so far!
I know about Wick rotation, but I’m curious about the converse—have you ever heard of someone using imaginary temperature?
It’s not even all that crazy—the Boltzmann distribution would just be sinuosidal. A cursory googling also turns up the notion of expanding phase diagrams of simple lattice models to the complex temperature plane. But I’ve never heard of an actual case where this would show up (unlike negative temperature which has justifying examples like lasers).
Thank you!
As a technique, there is so-called Matsubara frequency calculation using something like imaginary temperature (not exactly, but it is the closest thing I can think about).
From the physical point of view, the imaginary temperature would mean complex probabilities, which is a very strange thing. From a frequentist approach, they do not make sense at all. From bayesian approach, we potentially can define it, but still not clear what would they mean.
I figure it would be the same as complex electric fields etc—you just take the real part at the end.
Ok, but what would negative probability then be?
Good question :P