Ever since I read through the beginning of David Tong's statistical notes, I've been fascinated by how independent the notion of temperature is from laws of physics. To get a notion of "temperature of a system", basically all you need is 1/ a way to assign a set of possible microstates and macrostates (along with a probability distribution for them) to a system 2/ a notion of energy, that is, a quantity that is extensive (i.e. the energy of the combination of two systems is the sum of their individual energies) and conserved.
This got me thinking: in our universe, there are many more extensive, conserved quantities (mass, charge, linear/angular momentum along the x/y/z-axis...). What happens if you take the definition of temperature and just swap energy for one of those other quantities? I can't imagine no one has ever considered that!
https://www.damtp.cam.ac.uk/user/tong/statphys.html
#physics #StatisticalPhysics