  In this thesis, we present and discuss the quantum statistical foundations of
relativistic hydrodynamics with special emphasis on the entropy current. We
show that it is possible to provide a rigorous definition for this quantity in
the framework of relativistic quantum statistical mechanics and we put forward
a general method to calculate it at local thermodynamic equilibrium. The method
is based on the proof of existence of the thermodynamic potential current, a
usually tacitly understood hypothesis. We then apply the method for the entropy
current to the study of two different systems. The first system is a
relativistic quantum fluid at global thermodynamic equilibrium,
phenomenologically related to the quark-gluon plasma and, from a quantum field
theoretical standpoint, to the Unruh effect. The second systems is a
relativistic quantum fluid with boost invariance, also related to the
quark-gluon plasma and of great interest as the first solvable system out of
equilibrium. The thermal expectation value of the energy-momentum tensor as
well as the entropy current are calculated for both systems, and
renormalization is discussed.
