Equilibrium Spin Distribution From Detailed Balance

As the core ingredient for spin polarization, local equilibrium distribution function is derived from detailed balance principle. The kinetic theory interacting fermionic systems applied to Nambu--Jona-Lasinio model at quark level. Under semi-classical expansion with respect $\hbar$ and non-perturbative $N_c$, equations vector axial-vector functions are collision terms. It found that, an initially unpolarized system, non-zero polarization can be generated order of coupling between charges. requirement balance. arises thermal vorticity orthogonal particle momentum.