  We present an extension of relativistic single-particle distribution function
for weakly interacting particles at local thermodynamical equilibrium including
spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis
of the global equilibrium case, that at local thermodynamical equilibrium
particles acquire a net polarization proportional to the vorticity of the
inverse temperature four-vector field. The obtained formula for polarization
also implies that a steady gradient of temperature entails a polarization
orthogonal to particle momentum. The single-particle distribution function in
momentum space extends the so-called Cooper-Frye formula to particles with spin
1/2 and allows to predict their polarization in relativistic heavy ion
collisions at the freeze-out.
