= Thermal winding dominance of a free rotor
For the <quantum rotor>, low temperature makes the angular-momentum sum converge fastest: n=0 gives $Z\to1$. High temperature makes the temporal winding sum converge fastest: m=0 gives $Z\sim\sqrt{2\pi I/(\beta\hbar^2)}$. At low temperature many winding sectors contribute and cancel the vanishing fixed-endpoint prefactor. A zero-winding approximation valid at high temperature cannot be extended to low temperature merely because winding paths look geometrically longer.
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