Spin-thermal shear coupling in a relativistic fluid

We show that spin polarization of a fermion in relativistic fluid at local thermodynamic equilibrium can be generated by the symmetric derivative four-temperature vector, defined as thermal shear. As consequence, besides vorticity, acceleration and temperature gradient, also shear tensor contributes to particles fluid. This contribution which is entirely non-dissipative, adds well known term proportional vorticity may thus have important consequences for solution puzzles observed heavy ion collisions.