  The second law of thermodynamics is discussed and reformulated from a quantum
information theoretic perspective for open quantum systems using relative
entropy. Specifically, the relative entropy of a quantum state with respect to
equilibrium states is considered and its monotonicity property with respect to
an open quantum system evolution is used to obtain second law-like
inequalities. We discuss this first for generic quantum systems in contact with
a thermal bath and subsequently turn to a formulation suitable for the
description of local dynamics in a relativistic quantum field theory. A local
version of the second law similar to the one used in relativistic fluid
dynamics can be formulated with relative entropy or even relative entanglement
entropy in a space-time region bounded by two light cones. We also give an
outlook towards isolated quantum field theories and discuss the role of
entanglement for relativistic fluid dynamics.
