  We formulate the problem of approach to equilibrium in algebraic quantum
statistical mechanics and study some of its structural aspects, focusing on the
relation between the zeroth law of thermodynamics (approach to equilibrium) and
the second law (increase of entropy). Our main result is that approach to
equilibrium is necessarily accompanied by a strict increase of the specific
(mean) energy and entropy. In the course of our analysis, we introduce the
concept of quantum weak Gibbs state which is of independent interest.
