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