TLS - pseudospin or spin of $SU(2)$?
usually, TLS is thought to be a parametrization/representation by PSEUDOspin
if pseudospin is actual spin, then the particle with such a spin is a fermion
https://en.wikipedia.org/wiki/Spin-1/2
https://physics.stackexchange.com/questions/150590/spin-operators-commutation
- fixed-in-space spins
spin operators on different sites commuting
a paradox - a spin of a particle knows what statistics of two indistinguishable particles (two-particle wavefunction) must be
spin is a property of a single particle, q-statistics&indistinguishability is a property of two particles.
Yet the paradox is that property of two particles/statistics is the consequence of the property of one particle
On the other hand, https://en.wikipedia.org/wiki/Quantum_entanglement underlines that an independent spin does not exist for q-entangled two-particles wavefunction. Spin-half is even more special because https://en.wikipedia.org/wiki/Orientation_entanglement makes it entangled under normal $2\pi$ rotations.
Gibbs paradox for LEEs in glasses?
http://www.bourbaphy.fr/frohlich.pdf
https://www.pas.rochester.edu/assets/pdf/undergraduate/su-2s_double_covering_of_so-3.pdf