Cool, but not particularly surprising. The Feynman path integral descriptions of light and heavy water at finite temperatures are certainly quite different, and one can calculate thermodynamic state functions from simulations of FPI's in imaginary time (PIMD). Neat to see it worked out analytically though.

I have one question. The classical proton in this paper does not have "spin" ?
The proton and the neutron has the magnetic moment.
And the 4 pi rotation experiment of the spinning neutron shows the wave nature of the neutron spin.

The proton and the neutron are much heavier than the electron.
So, If the spin angular momentum is as big as about hbar, the spinning speed probably doesn't become faster than the speed of light. (if the spin of the proton is a real rotation.) (The Story of Spin)
The spin angular momentum is the constant. So if the radius of the (spin) rotation changes, the velocity of the proton changes?
Probably no one deny the wave nature of the proton and neutron, I think.
"Classical" in this paper means we use only the Maxwell's law, and don't use the de Broglie's theory?
But we should consider the de Broglie's theory, too?

So the classical proton in this paper doesn't contain the intrinsic movement such as "spin", does it?