
The Second and Third Laws 81
nal energy reaches a maximum. Then from eqn.(3.37) it follows that temperature can
be both positive and negative in these systems. In the vortex gas case, as elegantly
shown by Onsager, the negative temperature sector is not only physical but mani-
fests itself observationally in very novel ways [51]. But what is common to all these
systems with both positive and negative temperatures is that the two sectors do not
communicate to each other, and no smooth transformations connect them. Therefore
in effect, one is dealing with systems where the temperature is always of one sign.
In classical thermodynamics temperatures are ...