We put forward a general method to determine the entropy current of relativistic matter at local thermodynamic equilibrium in relativistic quantum statistical mechanics. Provided that the local equilibrium operator is bounded from below with non-degenerate lowest eigenvalue, it is proved that the entropy is extensive, namely it can be expressed as an integral of an entropy current on a 3-dimensional spacelike hypersurface. We then apply our method to the study of two systems of both theoretical and phenomenological concern. The former being a relativistic fluid at global thermodynamic equilibrium with acceleration, which is particularly interesting for it is related to the Unruh effect. The latter being a relativistic fluid at global thermodynamic equilibrium with boost invariance, the first case of an exactly solvable system at local thermodynamic equilibrium.