  We present a general method to determine the entropy current of relativistic
matter at local thermodynamic equilibrium in quantum statistical mechanics.
Provided that the local equilibrium operator is bounded from below and its
lowest lying eigenvector is non-degenerate, it is proved that, in general, the
logarithm of the partition function is extensive, meaning that it can be
expressed as the integral over a 3D space-like hypersurface of a vector
current, and that an entropy current exists. We work out a specific calculation
for a non-trivial case of global thermodynamic equilibrium, namely a system
with constant comoving acceleration, whose limiting temperature is the Unruh
temperature. We show that the integral of the entropy current in the right
Rindler wedge is the entanglement entropy.
